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

<div>Line superposition operation for <svg height="11.927pt" id="M45" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 11.727 11.927" width="11.727pt" 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="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z"></path></g></svg> denoted by <span class="nowrap"><svg height="12.5794pt" id="M46" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 35.0592 12.5794" width="35.0592pt" 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="M699 368C699 549 574 666 407 666C186 666 23 488 23 277C23 113 129 -3 288 -13L307 -26C431 -111 501 -139 533 -147C559 -154 613 -163 658 -164L666 -141C597 -111 507 -66 430 -11L416 -1C580 42 699 190 699 368ZM601 371C601 227 518 54 381 22L354 40L278 24C175 47 120 145 120 269C120 451 235 631 398 631C540 631 601 521 601 371Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.321,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g><g transform="matrix(.013,0,0,-0.013,14.267,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.765,0)"><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,-0.0091,25.422,3.132)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z"></path></g><g transform="matrix(.013,0,0,-0.013,30.368,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg>.</span></div>

Journal of Mathematics

fig1

Figure 1

Figure 1: Comparative Study of Generalized Sum Graphs via Degree-Based Topological Indices 