Fault-Tolerant Resolvability in Some Classes of Line Graphs

<div>The line graph <svg height="14.6294pt" id="M84" style="vertical-align:-5.34107pt" version="1.1" viewbox="-0.0498162 -9.28833 34.6559 14.6294" width="34.6559pt" 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="M822 650H589L583 622C660 617 677 607 674 561C672 534 664 481 647 390L600 137H596L273 650H126L120 622C176 620 194 615 207 594C221 571 225 557 214 504L161 257C141 166 129 112 121 85C108 42 83 30 29 28L23 0H260L266 28C193 33 173 42 176 89C178 122 186 172 202 255L256 527H259L583 -8H612L690 390C708 481 720 535 728 558C744 603 756 619 816 622L822 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,21.745,3.132)"><path d="M398 365C398 411 356 451 297 451C250 451 198 430 151 397C65 336 24 230 24 139C24 14 97 -12 148 -12C198 -12 284 7 373 104L355 130C306 84 246 53 198 53C132 53 111 109 111 163V189C209 211 398 261 398 365ZM317 351C317 308 273 262 117 225C134 338 189 383 221 399C230 404 249 407 263 407C295 407 317 389 317 351Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,25.54,5.233)"><path d="M513 91L497 125C461 87 438 71 424 71C416 71 410 77 419 106C440 174 459 243 472 310C497 441 467 454 445 454C419 454 393 443 360 424C319 400 237 344 180 265H178L196 336C217 421 207 454 182 454C146 454 84 416 25 354L42 318C66 342 103 368 113 368C119 368 124 362 117 333L31 -2L41 -12C59 -3 91 5 119 11C133 76 146 123 162 180C214 262 337 384 383 384C404 384 411 371 391 304C370 233 350 165 333 90C318 24 328 -12 359 -12C385 -12 449 23 513 91Z"></path></g><g transform="matrix(.013,0,0,-0.013,29.956,0)"><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> of a necklace graph.</div>

Mathematical Problems in Engineering

Fault-Tolerant Resolvability in Some Classes of Line Graphs

Figure 2