Investigation on Boron Alpha Nanotube by Studying Their M-Polynomial and Topological Indices

<div>Edge partition of boron <span class="nowrap"><svg height="6.1673pt" id="M76" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 7.51131 6.1673" width="7.51131pt" 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="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g></svg>-</span>nanotube (<span class="nowrap"><svg height="14.2314pt" id="M77" style="vertical-align:-5.282319pt" version="1.1" viewbox="-0.0498162 -8.94908 40.1795 14.2314" width="40.1795pt" 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="M401 353C473 367 557 406 557 502C557 551 535 592 498 616C460 640 410 650 333 650H41V615C112 608 121 602 121 516V134C121 49 112 42 35 35V0H289C372 0 449 14 500 43C556 74 593 126 593 193C593 288 517 335 401 349V353ZM253 363V553C253 574 255 589 262 596C268 602 284 609 307 609C361 609 415 575 415 484C415 401 372 363 276 363H253ZM253 323H273C386 323 445 276 445 182C445 84 382 43 326 42C273 41 253 62 253 136V323Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.312,3.132)"><path d="M558 106L533 129C501 84 476 67 464 67C446 67 435 116 414 239C457 297 508 367 550 440L539 451L484 438C458 390 429 338 404 300H402C375 407 351 451 285 451C168 451 24 312 24 153C24 56 66 -12 132 -12C206 -12 284 64 345 156H347C367 24 386 -12 422 -12C457 -12 503 7 558 106ZM338 206C272 99 215 56 173 56C140 56 116 96 116 170C116 303 194 405 255 405C304 405 324 299 338 206Z"></path></g><g transform="matrix(.013,0,0,-0.013,14.126,0)"><path d="M724 650H480V616C554 612 574 595 579 552C582 523 587 476 587 387V211H584L201 650H16V616C59 612 81 604 100 580S120 538 120 472V264C120 176 114 131 110 98C106 55 83 39 27 35V0H272V35C198 38 181 57 176 101C173 131 168 176 168 264V488H171L587 -10H635V387C635 476 641 523 644 554C649 599 670 613 724 616V650Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.782,0)"><path d="M616 481C611 545 606 633 605 675H580C563 656 549 650 523 650H121C92 650 79 653 64 675H39C37 624 31 551 27 478H64C77 528 89 562 106 579C120 596 138 606 221 606H255V133C255 48 245 42 161 35V0H487V35C399 42 389 48 389 133V606H434C493 606 518 601 536 583S568 531 580 479L616 481Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,32.147,3.132)"><path d="M270 0V32C208 38 203 43 203 110V703C146 688 72 674 15 667V637C70 630 75 628 75 567V110C75 45 70 41 10 32V0H270Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,34.686,3.132)"><path d="M534 -230V-198C472 -191 467 -186 467 -127V336C467 404 469 422 470 442L465 446C441 437 423 434 414 434C403 434 396 435 381 440C370 444 350 451 309 454C158 455 29 343 29 201C29 103 99 -12 259 -12L339 22V-126C339 -187 330 -190 260 -198V-230H534ZM339 58C327 52 317 50 303 50C247 50 170 115 170 235C170 358 226 413 271 413C293 413 319 398 339 372V58Z"></path></g></svg>).</span></div>

Journal of Mathematics

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Table 3

Table 3: Investigation on Boron Alpha Nanotube by Studying Their M-Polynomial and Topological Indices 