Comparative Study of Generalized Sum Graphs via Degree-Based Topological Indices

<table class="table-group" id="tab4"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left">TI’s</td><td class="align_center">Value of <svg height="11.7978pt" id="M297" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.5914 13.2276 11.7978" width="13.2276pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.151,-5.741)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g></svg></td><td class="align_center">Variability of <svg height="8.68572pt" id="M298" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 8.6074 8.68572" width="8.6074pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M640 650H413L406 622L438 617C475 611 483 605 463 571C422 503 346 400 296 333C264 403 215 529 199 575C189 604 191 614 228 618L262 622L271 650H30L23 622C90 615 97 609 119 553L212 321C222 295 223 285 218 259L193 127C176 39 167 33 82 28L76 0H350L356 28C266 36 257 40 275 127L303 266C308 290 314 302 328 322C396 418 454 493 498 546C551 610 565 616 631 622L640 650Z"></path></g></svg> is explained by <svg height="8.68572pt" id="M299" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 10.0819 8.68572" width="10.0819pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M748 650H522L515 622L546 617C580 611 587 604 565 575C518 513 469 451 419 393C376 474 349 534 330 580C318 609 325 612 361 618L383 622L392 650H151L144 622C214 616 224 612 257 543L360 327C270 218 187 124 159 95C106 40 92 34 26 28L17 0H252L259 28L236 31C189 37 188 47 209 78C249 136 308 210 377 294L478 79C494 44 487 37 449 32L418 28L409 0H673L680 28C596 34 591 39 554 116L436 361C526 469 574 521 604 553C659 612 669 614 739 622L748 650Z"></path></g></svg></td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left"><span style="width: 99.1058ptpx;"><svg height="12.4764pt" id="M300" style="vertical-align:-3.240271pt" version="1.1" viewbox="-0.0498162 -9.23613 99.1058 12.4764" width="99.1058pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M524 497C519 556 514 633 513 650H40V615C113 608 122 601 122 511V142C122 48 113 42 40 35V0H351V35C264 42 256 48 256 142V300H338C427 300 437 292 448 224H484V423H448C437 359 427 350 338 350H256V571C256 604 260 606 295 606H345C401 606 428 599 449 577C466 559 479 529 489 491L524 497Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.229,0)"><path d="M148 517C189 517 220 549 220 587C220 627 189 657 149 657C111 657 78 627 78 587C78 549 111 517 148 517ZM285 0V32C225 39 220 45 220 114V454C164 438 98 425 37 418V389C85 381 92 378 92 312V114C92 43 86 39 28 32V0H285Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.078,0)"><path d="M220 349V455C158 436 98 425 38 417V389C85 378 92 374 92 323V104C92 43 83 38 28 32V0H302V32C225 38 220 43 220 104V291C237 330 257 343 276 343C292 343 305 336 322 322C329 316 339 313 353 318C379 328 402 356 402 392C402 426 374 454 335 454C297 454 259 411 222 349H220Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.35,0)"><path d="M338 322C336 342 324 413 314 436C291 446 264 454 218 454C113 453 50 390 50 312C50 226 131 187 178 164C239 135 253 110 253 81C253 51 231 27 199 27C138 27 91 96 69 159L40 156C40 108 49 38 55 22C76 7 128 -12 181 -12C265 -12 360 37 360 136C360 214 306 249 225 284C174 307 151 330 151 361C151 393 176 415 202 415C249 415 281 374 308 313L338 322Z"></path></g><g transform="matrix(.013,0,0,-0.013,21.348,0)"><path d="M329 37L319 72C301 64 285 60 268 60C248 60 212 69 212 147V394H304C320 402 321 431 310 442H212V586L198 593L84 515V442H44L16 406L21 394H84V114C84 24 130 -12 207 -12C214 -12 230 -8 247 -1L329 37Z"></path></g><g transform="matrix(.013,0,0,-0.013,27.946,0)"><path d="M574 193C552 131 535 101 511 78C482 51 412 45 334 45C271 45 243 47 210 51C335 250 459 440 584 635L576 650H170C138 650 127 652 112 675H86C84 623 78 553 75 476L108 475C119 522 135 552 147 570C163 594 182 605 284 605H410C286 412 157 211 29 17L40 0H571C581 35 599 136 607 185L574 193Z"></path></g><g transform="matrix(.013,0,0,-0.013,36.024,0)"><path d="M465 45L455 77C444 72 433 69 421 69C404 69 389 81 389 128V293C389 349 380 392 337 425C310 445 280 454 239 454C182 443 111 409 73 383C51 366 38 353 38 335C38 309 74 285 101 285C121 285 136 293 143 319C151 350 160 374 171 388C180 400 191 406 205 406C241 406 265 371 265 308V278C242 258 165 234 106 212C54 192 30 168 30 116C30 54 81 -12 165 -12C185 -12 232 21 270 46C274 34 281 21 295 9C308 -3 329 -12 356 -12L465 45ZM265 79C249 67 238 63 223 63C200 63 163 84 163 139C163 174 179 192 210 208C231 219 247 229 265 239V79Z"></path></g><g transform="matrix(.013,0,0,-0.013,42.104,0)"><path d="M494 439C454 435 401 429 349 428C312 446 283 454 242 454H241C152 454 48 402 48 290C48 228 85 177 146 157C127 139 95 112 44 91C43 77 48 53 58 37C73 16 92 -3 133 -18C108 -34 82 -48 58 -68C38 -84 27 -100 27 -123C27 -178 85 -244 214 -244C347 -244 481 -153 481 -39C481 66 390 84 327 84C295 84 267 82 235 82C187 81 170 103 170 120C170 131 177 140 184 148C199 146 216 143 234 143C332 143 424 195 424 299C424 333 413 356 398 376L455 371C474 382 492 414 498 432L494 439ZM235 417C284 417 305 359 305 294C305 220 284 180 245 180C198 180 176 236 176 306C176 379 205 417 235 417ZM242 -21C280 -21 302 -23 329 -29C361 -38 385 -59 385 -95C385 -148 340 -189 264 -189C185 -189 135 -141 135 -92C135 -72 144 -57 158 -42C172 -26 194 -21 242 -21Z"></path></g><g transform="matrix(.013,0,0,-0.013,48.524,0)"><path d="M220 349V455C158 436 98 425 38 417V389C85 378 92 374 92 323V104C92 43 83 38 28 32V0H302V32C225 38 220 43 220 104V291C237 330 257 343 276 343C292 343 305 336 322 322C329 316 339 313 353 318C379 328 402 356 402 392C402 426 374 454 335 454C297 454 259 411 222 349H220Z"></path></g><g transform="matrix(.013,0,0,-0.013,53.796,0)"><path d="M400 123C365 93 327 80 288 80C216 80 157 134 153 241C251 245 374 254 392 257C414 260 420 273 421 293C421 375 351 454 258 454H257C203 454 148 427 104 383C62 341 30 278 30 202C30 87 103 -12 237 -12C279 -12 357 8 417 99L400 123ZM237 414C276 414 299 362 298 311C298 294 292 291 277 291C236 290 199 289 157 288C164 367 198 414 237 414Z"></path></g><g transform="matrix(.013,0,0,-0.013,59.498,0)"><path d="M196 417V703C139 687 58 673 7 667V636C63 632 68 623 68 566V24C137 -2 188 -12 244 -12C390 -12 504 97 504 243C504 355 418 454 297 454C277 454 261 447 233 434L196 417ZM196 382C211 387 221 389 238 389C301 389 365 339 365 212C365 87 316 27 262 28C230 29 207 59 201 75C198 83 196 94 196 108V382Z"></path></g><g transform="matrix(.013,0,0,-0.013,68.642,0)"><path d="M148 517C189 517 220 549 220 587C220 627 189 657 149 657C111 657 78 627 78 587C78 549 111 517 148 517ZM285 0V32C225 39 220 45 220 114V454C164 438 98 425 37 418V389C85 381 92 378 92 312V114C92 43 86 39 28 32V0H285Z"></path></g><g transform="matrix(.013,0,0,-0.013,72.491,0)"><path d="M549 0V32C497 40 491 42 491 105V294C491 394 441 454 360 454C331 454 312 445 282 426C260 412 240 396 220 383V456C161 439 95 425 39 418V390C87 380 92 377 92 317V109C92 42 88 41 26 32V0H267V32C225 38 220 42 220 104V346C246 366 268 377 294 377C330 377 363 355 363 283V113C363 42 358 38 316 32V0H549Z"></path></g><g transform="matrix(.013,0,0,-0.013,79.877,0)"><path d="M541 58L519 60C477 65 472 69 472 126V703C421 688 341 674 277 667V636C338 628 344 624 344 570V449C322 452 311 454 303 454C147 454 29 343 29 207C29 58 147 -12 233 -12C244 -12 259 -9 283 6L344 45V-13C423 10 517 22 541 26V58ZM344 80C322 66 307 64 289 64C243 64 171 111 171 234C171 386 248 412 271 412C301 412 328 395 344 360V80Z"></path></g><g transform="matrix(.013,0,0,-0.013,87.014,0)"><path d="M400 123C365 93 327 80 288 80C216 80 157 134 153 241C251 245 374 254 392 257C414 260 420 273 421 293C421 375 351 454 258 454H257C203 454 148 427 104 383C62 341 30 278 30 202C30 87 103 -12 237 -12C279 -12 357 8 417 99L400 123ZM237 414C276 414 299 362 298 311C298 294 292 291 277 291C236 290 199 289 157 288C164 367 198 414 237 414Z"></path></g><g transform="matrix(.013,0,0,-0.013,92.717,0)"><path d="M494 0V32C450 38 426 53 393 105L296 260C330 305 354 338 375 361C411 396 421 401 476 410V442H293V410C332 402 337 394 323 371C311 351 295 324 274 293L227 371C213 393 218 402 252 410V442H16V410C70 402 80 391 108 344L196 199C166 159 140 123 115 95C81 54 61 43 7 32V0H196V32C156 41 150 53 167 81C182 105 199 138 219 166L269 79C287 49 283 38 245 32V0H494Z"></path></g></svg></span></td><td class="align_center"><span style="width: 34.3917ptpx;"><svg height="8.55521pt" id="M301" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 34.3917 8.55521" width="34.3917pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,9.204,0)"><path d="M244 635C114 635 38 519 38 422C38 317 111 240 217 240C236 240 255 244 277 256L345 292C311 140 203 39 59 15L64 -15C89 -15 150 -5 204 17C339 72 440 202 440 386C440 521 368 635 244 635ZM228 602C326 602 352 479 352 390C352 370 351 347 348 324C327 308 293 296 258 296C174 296 124 369 124 458C124 517 152 602 228 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.445,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z"></path></g><g transform="matrix(.013,0,0,-0.013,21.686,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,27.926,0)"><path d="M249 635C141 635 70 555 70 471C70 401 114 353 179 316C143 294 106 267 90 252C68 231 45 202 45 157C45 50 130 -12 237 -12C322 -12 435 52 435 169C435 256 372 304 303 343C349 374 375 398 383 407C401 429 411 458 411 487C411 569 344 635 249 635ZM238 603C285 603 337 567 337 482C337 422 310 385 276 358C205 393 145 426 145 500C145 552 179 603 238 603ZM248 20C183 20 125 70 125 163C125 218 158 268 206 300C284 261 355 217 355 143C355 66 308 20 248 20Z"></path></g></svg></span></td><td class="align_center"><span style="width: 65.1698ptpx;"><svg height="11.3998pt" id="M302" style="vertical-align:-3.050981pt" version="1.1" viewbox="-0.0498162 -8.34882 65.1698 11.3998" width="65.1698pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M244 635C114 635 38 519 38 422C38 317 111 240 217 240C236 240 255 244 277 256L345 292C311 140 203 39 59 15L64 -15C89 -15 150 -5 204 17C339 72 440 202 440 386C440 521 368 635 244 635ZM228 602C326 602 352 479 352 390C352 370 351 347 348 324C327 308 293 296 258 296C174 296 124 369 124 458C124 517 152 602 228 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.241,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.482,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.446,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.861,0)"><path d="M212 391V464C146 445 80 427 26 418V388C75 381 84 376 84 321V-128C84 -184 80 -192 16 -198V-230H294V-198C216 -191 212 -184 212 -127V0C227 -6 249 -12 274 -12C402 17 517 114 517 261C517 357 454 454 336 454C319 454 301 447 281 435L212 391ZM212 354C229 369 250 378 275 378C324 378 385 333 385 210C385 106 347 38 293 38C268 38 231 59 212 77V354Z"></path></g><g transform="matrix(.013,0,0,-0.013,30.998,0)"><path d="M400 123C365 93 327 80 288 80C216 80 157 134 153 241C251 245 374 254 392 257C414 260 420 273 421 293C421 375 351 454 258 454H257C203 454 148 427 104 383C62 341 30 278 30 202C30 87 103 -12 237 -12C279 -12 357 8 417 99L400 123ZM237 414C276 414 299 362 298 311C298 294 292 291 277 291C236 290 199 289 157 288C164 367 198 414 237 414Z"></path></g><g transform="matrix(.013,0,0,-0.013,36.701,0)"><path d="M220 349V455C158 436 98 425 38 417V389C85 378 92 374 92 323V104C92 43 83 38 28 32V0H302V32C225 38 220 43 220 104V291C237 330 257 343 276 343C292 343 305 336 322 322C329 316 339 313 353 318C379 328 402 356 402 392C402 426 374 454 335 454C297 454 259 411 222 349H220Z"></path></g><g transform="matrix(.013,0,0,-0.013,41.972,0)"><path d="M399 120C363 89 334 79 292 79S154 123 154 256C154 363 199 401 238 401C266 401 298 385 339 349C348 341 354 338 361 338C378 338 404 364 404 393C405 407 401 419 386 429C369 443 336 454 300 454H299C261 454 196 440 130 392C67 345 29 274 29 201C29 92 109 -12 246 -12C307 -12 372 31 418 96L399 120Z"></path></g><g transform="matrix(.013,0,0,-0.013,47.479,0)"><path d="M400 123C365 93 327 80 288 80C216 80 157 134 153 241C251 245 374 254 392 257C414 260 420 273 421 293C421 375 351 454 258 454H257C203 454 148 427 104 383C62 341 30 278 30 202C30 87 103 -12 237 -12C279 -12 357 8 417 99L400 123ZM237 414C276 414 299 362 298 311C298 294 292 291 277 291C236 290 199 289 157 288C164 367 198 414 237 414Z"></path></g><g transform="matrix(.013,0,0,-0.013,53.181,0)"><path d="M549 0V32C497 40 491 42 491 105V294C491 394 441 454 360 454C331 454 312 445 282 426C260 412 240 396 220 383V456C161 439 95 425 39 418V390C87 380 92 377 92 317V109C92 42 88 41 26 32V0H267V32C225 38 220 42 220 104V346C246 366 268 377 294 377C330 377 363 355 363 283V113C363 42 358 38 316 32V0H549Z"></path></g><g transform="matrix(.013,0,0,-0.013,60.567,0)"><path d="M329 37L319 72C301 64 285 60 268 60C248 60 212 69 212 147V394H304C320 402 321 431 310 442H212V586L198 593L84 515V442H44L16 406L21 394H84V114C84 24 130 -12 207 -12C214 -12 230 -8 247 -1L329 37Z"></path></g></svg></span></td></tr><tr><td class="align_left">Second Zagreb index</td><td class="align_center">0.908 0</td><td class="align_center">90.8 percent</td></tr><tr><td class="align_left">Forgotten Zagreb index</td><td class="align_center">0.832 3</td><td class="align_center">83.23 percent</td></tr><tr><td class="align_left">Hyper Zagreb index</td><td class="align_center">0.947 8</td><td class="align_center">94.78 percent</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Square of correlation coefficient between <svg height="16.0647pt" id="M295" style="vertical-align:-6.776369pt" version="1.1" viewbox="-0.0498162 -9.28833 50.0189 16.0647" width="50.0189pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.656,3.132)"><path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,11.27,5.233)"><path d="M318 -137C221 -59 159 100 159 272S220 600 318 680L294 710C146 612 80 452 80 273V272C80 91 146 -72 294 -168L318 -137Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,13.675,5.233)"><path d="M756 349C756 552 603 667 429 667C202 667 25 496 25 288C25 117 151 -5 319 -18L340 -31C492 -128 548 -147 590 -156C612 -161 675 -173 722 -175L730 -148C665 -119 534 -59 480 -19L460 -4C627 37 756 172 756 349ZM648 350C648 207 555 51 418 29L387 43L309 29C201 51 132 153 132 284C132 483 262 620 419 620C570 620 648 517 648 350Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,18.42,6.668)"><path d="M586 441L561 454L490 441C465 394 436 344 411 304H409C381 410 356 454 288 454C168 454 25 314 25 154C25 57 66 -12 137 -12C210 -12 287 49 355 137H357C373 31 393 -12 433 -12C470 -12 515 3 572 105L558 117C536 82 513 68 501 68C474 68 459 112 431 213C480 278 539 364 586 441ZM344 208C279 102 220 57 177 57C144 57 120 95 120 170C120 303 197 405 258 405C310 405 333 278 344 208Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,22.904,5.233)"><path d="M291 272C291 452 228 611 76 710L51 680C147 602 211 444 211 272S151 -55 51 -137L76 -168C227 -66 291 91 291 272Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.359,0)"><path d="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 675V703H120V-163H290Z"></path></g><g transform="matrix(.013,0,0,-0.013,30.844,0)"><path d="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,37.5,3.132)"><path d="M781 91L765 118C733 86 702 70 693 70C686 70 685 77 692 106L738 297C772 439 736 451 712 451S675 445 647 431C605 410 526 356 452 257H450L459 294C491 426 459 451 429 451C403 451 386 445 361 431C312 404 239 343 170 253H168L188 333C208 411 205 451 175 451C148 451 85 417 24 346L39 318C57 338 100 374 112 374C120 374 122 372 115 339C91 226 62 112 28 -6L37 -12C59 -4 87 3 114 6C125 68 142 127 154 168C184 227 316 383 372 383C397 383 396 366 381 289C362 192 338 92 312 -6L317 -12C339 -5 367 3 396 6L434 170C468 234 598 383 650 383C668 383 676 369 664 319L609 90C593 23 600 -12 629 -12C654 -12 722 23 781 91Z"></path></g><g transform="matrix(.013,0,0,-0.013,45.351,0)"><path d="M226 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H226Z"></path></g></svg> and <span class="nowrap"><svg height="12.5794pt" id="M296" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 35.4911 12.5794" width="35.4911pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.656,3.132)"><path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.831,0)"><path d="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 675V703H120V-163H290Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.316,0)"><path d="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,22.972,3.132)"><path d="M781 91L765 118C733 86 702 70 693 70C686 70 685 77 692 106L738 297C772 439 736 451 712 451S675 445 647 431C605 410 526 356 452 257H450L459 294C491 426 459 451 429 451C403 451 386 445 361 431C312 404 239 343 170 253H168L188 333C208 411 205 451 175 451C148 451 85 417 24 346L39 318C57 338 100 374 112 374C120 374 122 372 115 339C91 226 62 112 28 -6L37 -12C59 -4 87 3 114 6C125 68 142 127 154 168C184 227 316 383 372 383C397 383 396 366 381 289C362 192 338 92 312 -6L317 -12C339 -5 367 3 396 6L434 170C468 234 598 383 650 383C668 383 676 369 664 319L609 90C593 23 600 -12 629 -12C654 -12 722 23 781 91Z"></path></g><g transform="matrix(.013,0,0,-0.013,30.823,0)"><path d="M226 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H226Z"></path></g></svg>.</span></div>

Journal of Mathematics

tab4

Table 4

Table 4: Comparative Study of Generalized Sum Graphs via Degree-Based Topological Indices 