Connection Number- Based Topological Indices of Cartesian Product of Graphs

<table class="table-group" id="tab5"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left">S.R</td><td class="align_center"><span style="width: 55.5621ptpx;"><svg height="15.8912pt" id="M112" style="vertical-align:-5.93481pt" version="1.1" viewbox="-0.0498162 -9.95639 55.5621 15.8912" width="55.5621pt" 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="M697 650H468L461 623L492 619C539 613 547 605 518 546C481 471 367 264 278 116H276C239 278 197 500 186 567C180 604 185 613 226 619L252 623L260 650H24L17 623C78 617 92 613 108 533L216 -11H247C365 200 515 462 560 529C616 612 624 615 689 623L697 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.224,-5.741)"><path d="M387 400C387 425 348 451 303 451C247 451 176 414 132 376C69 322 24 228 24 148C24 43 74 -12 147 -12C211 -12 301 33 363 103L346 128C319 99 249 51 193 51C148 51 112 84 112 165C112 230 130 287 154 330C170 359 199 400 243 400C277 400 304 383 326 354C333 345 343 343 354 348C378 360 387 382 387 400Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.332,3.784)"><path d="M309 -142C211 -61 151 99 151 271S210 601 309 683L288 710C141 611 75 451 75 272V271C75 90 141 -72 288 -169L309 -142Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.59,3.784)"><path d="M487 458L455 460C436 434 425 433 397 433C331 433 279 437 225 437C103 437 52 374 24 338L49 312C100 363 152 379 229 374C210 308 184 213 163 117C158 94 156 74 156 58C156 6 180 -12 211 -12C261 -12 313 27 348 68L332 99C307 76 285 64 267 64C252 64 236 86 250 148L301 373C320 373 344 369 364 369C399 369 435 370 450 372C458 386 470 411 487 458Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,15.133,3.784)"><path d="M309 -142C211 -61 151 99 151 271S210 601 309 683L288 710C141 611 75 451 75 272V271C75 90 141 -72 288 -169L309 -142Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.391,3.784)"><path d="M504 89L488 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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,-0.0065,44.555,5.885)"><path d="M452 139L416 148C386 81 373 77 319 77H141L282 220C372 312 414 373 414 464C414 569 332 635 240 635C181 635 132 609 101 574L42 493L70 467C98 506 143 562 209 562C280 562 324 515 324 435C324 347 261 272 197 197C148 139 89 84 34 29V0H417L452 139Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,48.276,3.784)"><path d="M283 271C283 451 220 610 70 710L48 683C146 603 207 443 207 271S149 -59 48 -142L70 -169C220 -67 283 90 283 271Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,51.534,3.784)"><path d="M283 271C283 451 220 610 70 710L48 683C146 603 207 443 207 271S149 -59 48 -142L70 -169C220 -67 283 90 283 271Z"></path></g></svg></span></td><td class="align_center">Number of vertices</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">1</td><td class="align_center"><span style="width: 13.6034ptpx;"><svg height="13.8999pt" id="M113" style="vertical-align:-3.94351pt" version="1.1" viewbox="-0.0498162 -9.95639 13.6034 13.8999" width="13.6034pt" 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="M697 650H468L461 623L492 619C539 613 547 605 518 546C481 471 367 264 278 116H276C239 278 197 500 186 567C180 604 185 613 226 619L252 623L260 650H24L17 623C78 617 92 613 108 533L216 -11H247C365 200 515 462 560 529C616 612 624 615 689 623L697 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.224,-5.741)"><path d="M387 400C387 425 348 451 303 451C247 451 176 414 132 376C69 322 24 228 24 148C24 43 74 -12 147 -12C211 -12 301 33 363 103L346 128C319 99 249 51 193 51C148 51 112 84 112 165C112 230 130 287 154 330C170 359 199 400 243 400C277 400 304 383 326 354C333 345 343 343 354 348C378 360 387 382 387 400Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.332,3.784)"><path d="M397 380C406 395 404 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133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M393 379C402 394 400 411 393 422C384 437 365 448 348 448C301 448 237 372 186 285H182L193 335C210 408 205 448 178 448C150 448 80 402 29 344L45 321C80 355 114 373 122 373C128 373 130 365 124 330C106 228 76 98 50 -5L57 -12C82 -5 112 3 132 6L172 203C196 256 234 304 254 329C275 355 293 367 306 367C318 367 330 360 342 348C347 343 355 343 365 350S386 367 393 379Z"></path></g></svg></span></td></tr><tr><td class="align_left">3</td><td class="align_center"><span style="width: 16.3058ptpx;"><svg height="13.8999pt" id="M117" style="vertical-align:-3.94351pt" version="1.1" viewbox="-0.0498162 -9.95639 16.3058 13.8999" width="16.3058pt" 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="M697 650H468L461 623L492 619C539 613 547 605 518 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<div>Partitioning of vertices on the bases of connection numbers.</div>

Journal of Mathematics

tab5

Table 5

Table 5: Connection Number- Based Topological Indices of Cartesian Product of Graphs 