M-Polynomials and Topological Indices for Line Graphs of Chain Silicate Network and H-Naphtalenic Nanotubes

<div>M-Polynomial of line graph of H-naphtalenic nanotubes (<span class="nowrap"><svg height="12.7178pt" id="M197" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 80.8583 12.7178" width="80.8583pt" 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="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.185,0)"><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,-0.013,11.683,0)"><path d="M719 650H483V622C553 619 576 606 581 560C585 532 588 487 588 394V148H585L167 650H20V622C67 618 88 610 109 585C127 562 129 557 129 484V264C129 173 126 124 123 93C118 44 92 31 35 28V0H272V28C204 32 181 44 176 95C173 124 170 172 170 264V515H172L598 -9H629V394C629 487 631 532 635 563C639 606 663 619 719 622V650Z"></path></g><g transform="matrix(.013,0,0,-0.013,21.342,0)"><path d="M46 650V622C120 617 128 613 128 525V125C128 42 120 34 40 28V0H311V28C221 34 212 39 212 124V281L286 262C297 261 316 261 331 263C429 275 526 338 526 468C526 533 501 579 462 609C422 638 364 650 293 650H46ZM212 559C212 588 215 600 223 606C230 613 251 618 279 618C361 618 430 572 430 464C430 337 350 302 285 302C252 302 225 309 212 314V559Z"></path></g><g transform="matrix(.013,0,0,-0.013,28.596,0)"><path d="M729 650H468V622C546 615 554 610 554 527V365H213V527C213 610 221 616 297 622V650H38V622C120 616 128 611 128 527V123C128 39 120 34 40 28V0H303V28C221 34 213 40 213 123V322H554V123C554 39 546 34 460 28V0H728V28C647 34 639 39 639 123V527C639 610 647 615 729 622V650Z"></path></g><g transform="matrix(.013,0,0,-0.013,38.554,0)"><path d="M655 0V28C585 35 563 50 517 120C469 193 414 280 360 366C427 469 460 516 481 545C526 604 545 614 619 622V650H391V622C457 614 462 604 438 560C411 511 381 463 339 398C295 466 258 523 225 580C210 606 211 615 272 622V650H26V622C98 614 111 603 154 538C189 482 235 408 288 324C200 188 149 116 124 85C95 47 64 34 7 28V0H236V28C169 36 164 46 188 89C220 148 261 217 310 291C372 193 417 118 442 77C461 44 454 35 392 28V0H655Z"></path></g><g transform="matrix(.013,0,0,-0.013,47.188,0)"><path d="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 675V703H120V-163H290Z"></path></g><g transform="matrix(.013,0,0,-0.013,51.674,0)"><path d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z"></path></g><g transform="matrix(.013,0,0,-0.013,58.941,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,64.084,0)"><path d="M556 393C556 426 537 448 514 448C496 448 478 435 471 420C468 414 462 401 466 394C473 382 480 368 480 346C480 268 392 143 338 67H336C329 163 319 253 309 330S286 448 254 448C215 448 160 383 127 337L143 311C167 344 200 373 208 373S222 365 229 320C246 214 264 66 268 -20C219 -83 131 -171 17 -239L25 -261L137 -235C248 -110 273 -79 335 8C384 77 481 215 520 287C544 332 556 363 556 393Z"></path></g><g transform="matrix(.013,0,0,-0.013,71.613,0)"><path d="M226 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H226Z"></path></g><g transform="matrix(.013,0,0,-0.013,76.098,0)"><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

fig9

Figure 9

Figure 9: M-Polynomials and Topological Indices for Line Graphs of Chain Silicate Network and H-Naphtalenic Nanotubes 