Hosoya and Harary Polynomials of <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.9939pt" id="M1" height="15.2545pt" version="1.1" viewBox="-0.0657574 -12.2606 185.793 15.2545" width="185.793pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-85" d="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z"/></g><g transform="matrix(.017,0,0,-0.017,10.936,0)"><path id="g113-80" d="M699 369C699 549 575 666 407 666C186 666 23 488 23 278C23 101 145 -16 312 -16C535 -16 699 153 699 369ZM600 373C600 210 500 19 321 19C186 19 120 129 120 272C120 450 232 631 399 631C541 631 600 522 600 373Z"/></g><g transform="matrix(.017,0,0,-0.017,22.466,0)"><path id="g113-89" d="M748 650H522L515 622L546 617C580 611 587 604 565 575C518 513 469 451 419 393C376 474 349 534 330 580C318 609 325 612 361 618L383 622L392 650H151L144 622C214 616 224 612 257 543L360 327C270 218 187 124 159 95C106 40 92 34 26 28L17 0H252L259 28L236 31C189 37 188 47 209 78C249 136 308 210 377 294L478 79C494 44 487 37 449 32L418 28L409 0H673L680 28C596 34 591 39 554 116L436 361C526 469 574 521 604 553C659 612 669 614 739 622L748 650Z"/></g><g transform="matrix(.017,0,0,-0.017,35.594,0)"><path id="g113-41" d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"/></g><g transform="matrix(.017,0,0,-0.017,41.531,0)"><path id="g113-111" d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z"/></g><g transform="matrix(.017,0,0,-0.017,50.145,0)"><path id="g113-42" d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"/></g><g transform="matrix(.017,0,0,-0.017,56.083,0)"><path id="g113-45" 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"/></g><g transform="matrix(.017,0,0,-0.017,62.872,0)"><path id="g113-83" d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z"/></g><g transform="matrix(.017,0,0,-0.017,73.632,0)"><use xlink:href="#g113-85"/></g><g transform="matrix(.017,0,0,-0.017,84.568,0)"><use xlink:href="#g113-80"/></g><g transform="matrix(.017,0,0,-0.017,96.099,0)"><use xlink:href="#g113-89"/></g><g transform="matrix(.017,0,0,-0.017,109.226,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.017,0,0,-0.017,115.163,0)"><use xlink:href="#g113-111"/></g><g transform="matrix(.017,0,0,-0.017,123.778,0)"><use xlink:href="#g113-42"/></g><g transform="matrix(.017,0,0,-0.017,129.715,0)"><use xlink:href="#g113-45"/></g><g transform="matrix(.017,0,0,-0.017,136.504,0)"><use xlink:href="#g113-85"/></g><g transform="matrix(.017,0,0,-0.017,147.268,0)"><path id="g113-84" d="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 309 307 360L276 382C223 419 179 455 179 516C179 576 221 632 293 632C379 632 410 564 418 487L448 490C446 536 446 592 449 634Z"/></g><g transform="matrix(.017,0,0,-0.017,155.023,0)"><path id="g113-77" 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"/></g><g transform="matrix(.017,0,0,-0.017,164.508,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.017,0,0,-0.017,170.445,0)"><use xlink:href="#g113-111"/></g><g transform="matrix(.017,0,0,-0.017,179.059,0)"><use xlink:href="#g113-42"/></g></svg> and <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.9939pt" id="M2" height="15.2545pt" version="1.1" viewBox="-0.0657574 -12.2606 59.6071 15.2545" width="59.6071pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><use xlink:href="#g113-83"/></g><g transform="matrix(.017,0,0,-0.017,10.759,0)"><use xlink:href="#g113-85"/></g><g transform="matrix(.017,0,0,-0.017,21.524,0)"><use xlink:href="#g113-84"/></g><g transform="matrix(.017,0,0,-0.017,29.279,0)"><use xlink:href="#g113-77"/></g><g transform="matrix(.017,0,0,-0.017,38.763,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.017,0,0,-0.017,44.7,0)"><use xlink:href="#g113-111"/></g><g transform="matrix(.017,0,0,-0.017,53.315,0)"><use xlink:href="#g113-42"/></g></svg>

<div>Modified hyper Wiener index of <span class="nowrap"><svg height="9.16851pt" id="M354" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.96212 27.1627 9.16851" width="27.1627pt" 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="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.285,0)"><path d="M699 369C699 549 575 666 407 666C186 666 23 488 23 278C23 101 145 -16 312 -16C535 -16 699 153 699 369ZM600 373C600 210 500 19 321 19C186 19 120 129 120 272C120 450 232 631 399 631C541 631 600 522 600 373Z"></path></g><g transform="matrix(.013,0,0,-0.013,17.02,0)"><path d="M748 650H522L515 622L546 617C580 611 587 604 565 575C518 513 469 451 419 393C376 474 349 534 330 580C318 609 325 612 361 618L383 622L392 650H151L144 622C214 616 224 612 257 543L360 327C270 218 187 124 159 95C106 40 92 34 26 28L17 0H252L259 28L236 31C189 37 188 47 209 78C249 136 308 210 377 294L478 79C494 44 487 37 449 32L418 28L409 0H673L680 28C596 34 591 39 554 116L436 361C526 469 574 521 604 553C659 612 669 614 739 622L748 650Z"></path></g></svg>.</span></div>

Discrete Dynamics in Nature and Society

tab8

Table 8

Table 8: Hosoya and Harary Polynomials of <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.9939pt" id="M1" height="15.2545pt" version="1.1" viewBox="-0.0657574 -12.2606 185.793 15.2545" width="185.793pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-85" d="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z"/></g><g transform="matrix(.017,0,0,-0.017,10.936,0)"><path id="g113-80" d="M699 369C699 549 575 666 407 666C186 666 23 488 23 278C23 101 145 -16 312 -16C535 -16 699 153 699 369ZM600 373C600 210 500 19 321 19C186 19 120 129 120 272C120 450 232 631 399 631C541 631 600 522 600 373Z"/></g><g transform="matrix(.017,0,0,-0.017,22.466,0)"><path id="g113-89" d="M748 650H522L515 622L546 617C580 611 587 604 565 575C518 513 469 451 419 393C376 474 349 534 330 580C318 609 325 612 361 618L383 622L392 650H151L144 622C214 616 224 612 257 543L360 327C270 218 187 124 159 95C106 40 92 34 26 28L17 0H252L259 28L236 31C189 37 188 47 209 78C249 136 308 210 377 294L478 79C494 44 487 37 449 32L418 28L409 0H673L680 28C596 34 591 39 554 116L436 361C526 469 574 521 604 553C659 612 669 614 739 622L748 650Z"/></g><g transform="matrix(.017,0,0,-0.017,35.594,0)"><path id="g113-41" d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"/></g><g transform="matrix(.017,0,0,-0.017,41.531,0)"><path id="g113-111" d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z"/></g><g transform="matrix(.017,0,0,-0.017,50.145,0)"><path id="g113-42" d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"/></g><g transform="matrix(.017,0,0,-0.017,56.083,0)"><path id="g113-45" 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"/></g><g transform="matrix(.017,0,0,-0.017,62.872,0)"><path id="g113-83" d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z"/></g><g transform="matrix(.017,0,0,-0.017,73.632,0)"><use xlink:href="#g113-85"/></g><g transform="matrix(.017,0,0,-0.017,84.568,0)"><use xlink:href="#g113-80"/></g><g transform="matrix(.017,0,0,-0.017,96.099,0)"><use xlink:href="#g113-89"/></g><g transform="matrix(.017,0,0,-0.017,109.226,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.017,0,0,-0.017,115.163,0)"><use xlink:href="#g113-111"/></g><g transform="matrix(.017,0,0,-0.017,123.778,0)"><use xlink:href="#g113-42"/></g><g transform="matrix(.017,0,0,-0.017,129.715,0)"><use xlink:href="#g113-45"/></g><g transform="matrix(.017,0,0,-0.017,136.504,0)"><use xlink:href="#g113-85"/></g><g transform="matrix(.017,0,0,-0.017,147.268,0)"><path id="g113-84" d="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 309 307 360L276 382C223 419 179 455 179 516C179 576 221 632 293 632C379 632 410 564 418 487L448 490C446 536 446 592 449 634Z"/></g><g transform="matrix(.017,0,0,-0.017,155.023,0)"><path id="g113-77" 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"/></g><g transform="matrix(.017,0,0,-0.017,164.508,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.017,0,0,-0.017,170.445,0)"><use xlink:href="#g113-111"/></g><g transform="matrix(.017,0,0,-0.017,179.059,0)"><use xlink:href="#g113-42"/></g></svg> and <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.9939pt" id="M2" height="15.2545pt" version="1.1" viewBox="-0.0657574 -12.2606 59.6071 15.2545" width="59.6071pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><use xlink:href="#g113-83"/></g><g transform="matrix(.017,0,0,-0.017,10.759,0)"><use xlink:href="#g113-85"/></g><g transform="matrix(.017,0,0,-0.017,21.524,0)"><use xlink:href="#g113-84"/></g><g transform="matrix(.017,0,0,-0.017,29.279,0)"><use xlink:href="#g113-77"/></g><g transform="matrix(.017,0,0,-0.017,38.763,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.017,0,0,-0.017,44.7,0)"><use xlink:href="#g113-111"/></g><g transform="matrix(.017,0,0,-0.017,53.315,0)"><use xlink:href="#g113-42"/></g></svg>

Discrete Dynamics in Nature and Society

Hosoya and Harary Polynomials of and

Table 8