Complete Characterization of Resistance Distance for Linear Octagonal Networks

<div>The network <span class="nowrap"><svg height="15.471pt" id="M141" style="vertical-align:-3.9435pt" version="1.1" viewbox="-0.0498162 -11.5275 17.7556 15.471" width="17.7556pt" 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="M962 650H739L732 622L760 619C812 613 819 604 798 552C760 457 671 267 606 131H604L511 638H480L237 131H233L183 554C177 607 183 614 226 619L248 622L257 650H24L17 622C88 615 92 611 103 524L173 -11H203L450 491H453L543 -11H575L839 529C882 609 886 613 953 622L962 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.669,-5.741)"><path d="M457 455H370L403 612H360L326 455H218L252 612H210L175 455H77L68 394H161L132 257H31L20 196H117L77 19H120L159 196H268L230 19H272L311 196H402L412 257H325L355 394H447L457 455ZM313 394L283 257H175L204 394H313Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.777,3.784)"><path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"></path></g></svg>.</span></div>

Complexity

fig8

Figure 8

Figure 8: Complete Characterization of Resistance Distance for Linear Octagonal Networks 