Various Uses of Topological Invariants in Jahangir Graph <i>J</i><sub><i>β</i>,<i>α</i></sub>

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left">(<i>d</i> (<i>u</i>), <i>d</i> (<span class="nowrap"><svg height="6.04987pt" id="M27" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="M219 86C216 168 211 250 206 337C201 410 189 448 163 448C131 448 79 396 43 344L60 322C91 359 110 375 118 375S132 358 136 298C141 238 152 81 155 -12H182C242 62 331 177 390 258C435 321 451 360 451 391C450 424 432 448 408 448C390 448 372 435 366 419C362 410 362 401 366 394C373 383 376 367 376 350C376 283 262 138 221 86H219Z"></path></g></svg>))</span></td><td class="align_center">Frequency</td><td class="align_center"><span style="width: 28.5364ptpx;"><svg height="12.5794pt" id="M28" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 28.5364 12.5794" width="28.5364pt" 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="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.15,3.132)"><path d="M722 297H451L442 267C561 257 561 253 547 182L531 98C521 44 465 24 390 24C228 24 130 134 130 296C130 482 252 628 465 628C592 628 657 579 656 458L692 461C695 540 699 605 702 631C664 642 590 667 492 667C203 667 24 502 24 285C24 93 170 -17 368 -17C464 -17 543 11 617 28C613 43 612 68 620 106L635 182C649 255 652 258 716 268L722 297Z"></path></g><g transform="matrix(.013,0,0,-0.013,13.978,0)"><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,-0.013,18.476,0)"><path d="M391 364C391 409 353 448 295 448C249 448 198 426 152 393C65 331 23 225 23 139C23 14 96 -12 146 -12C198 -12 280 9 367 101L351 124C300 78 242 48 194 48C129 48 109 107 109 162V191C208 213 391 266 391 364ZM313 350C313 305 268 261 113 223C132 334 187 381 217 398C227 404 244 405 261 405C290 405 313 385 313 350Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.858,0)"><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></td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">(2, 2)</td><td class="align_center">9</td><td class="align_center">2</td></tr><tr><td class="align_left">(3, 2)</td><td class="align_center">12</td><td class="align_center">3</td></tr><tr><td class="align_left">(3, 3)</td><td class="align_center">3</td><td class="align_center">4</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>The bidistance edge partition.</div>

Journal of Mathematics

tab2

Table 2

Table 2: Various Uses of Topological Invariants in Jahangir Graph <i>J</i><sub><i>β</i>,<i>α</i></sub> 

Journal of Mathematics

Various Uses of Topological Invariants in Jahangir Graph Jβ,α

Table 2

Various Uses of Topological Invariants in Jahangir Graph J_β,α