On Hamilton-Connectivity and Detour Index of Certain Families of Convex Polytopes

<div>The <span class="nowrap"><svg height="6.37608pt" id="M97" style="vertical-align:-0.2324901pt" version="1.1" viewbox="-0.0498162 -6.14359 6.02377 6.37608" width="6.02377pt" 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="M213 67C239 136 257 225 255 300C253 353 242 447 164 447C112 447 54 389 41 319L67 309C90 362 117 377 134 377C184 377 189 277 190 239C193 153 164 43 146 -12H176C278 73 450 253 450 390C450 439 410 463 396 463C384 463 380 459 382 449C385 440 389 415 389 402C389 284 312 146 216 67H213Z"></path></g></svg>-</span>dimensional convex polytope <span class="nowrap"><svg height="11.9453pt" id="M98" style="vertical-align:-3.309401pt" version="1.1" viewbox="-0.0498162 -8.6359 14.8574 11.9453" width="14.8574pt" 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="M828 650H570L564 622C646 614 650 609 634 524L604 366H253L281 524C296 608 308 615 382 622L388 650H132L126 622C211 615 214 609 198 524L121 122C106 42 102 35 23 28L17 0H276L282 28C196 35 191 40 206 122L243 324H597L559 123C544 42 537 35 452 28L446 0H710L716 28C632 35 628 43 643 122L719 524C735 610 741 615 822 622L828 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.075,3.132)"><path d="M213 67C239 136 257 225 255 300C253 353 242 447 164 447C112 447 54 389 41 319L67 309C90 362 117 377 134 377C184 377 189 277 190 239C193 153 164 43 146 -12H176C278 73 450 253 450 390C450 439 410 463 396 463C384 463 380 459 382 449C385 440 389 415 389 402C389 284 312 146 216 67H213Z"></path></g></svg>.</span></div>

Mathematical Problems in Engineering

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Figure 2

Figure 2: On Hamilton-Connectivity and Detour Index of Certain Families of Convex Polytopes 