Total Face Irregularity Strength of Certain Graphs

<div>(a) Triangular graph <svg height="14.0944pt" id="M298" style="vertical-align:-5.341061pt" version="1.1" viewbox="-0.0498162 -8.75334 23.1391 14.0944" width="23.1391pt" 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="M592 498C586 556 582 629 581 675H560C545 656 537 650 510 650H115C87 650 74 652 60 675H40C38 620 33 555 28 495H57C69 539 77 568 89 585C102 607 122 616 205 616H267V123C267 44 259 34 168 28V0H454V28C360 34 352 44 352 123V616H422C498 616 514 608 531 584C542 568 552 543 562 495L592 498Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.917,0)"><path d="M692 302H438V274C537 267 543 260 543 188V103C543 61 531 48 511 37C489 26 458 20 424 20C231 20 146 188 146 333C146 517 258 630 411 630C507 630 582 597 606 474L634 480C627 546 622 601 619 636C586 643 510 665 426 665C230 665 44 552 44 321C44 122 191 -15 411 -15C491 -15 573 7 635 21C629 49 628 81 628 116V202C628 261 632 266 692 274V302Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,18.82,5.233)"><path d="M436 222C436 297 385 359 295 376V378C320 391 343 407 363 428S394 474 394 501C394 578 333 635 239 635C186 635 138 610 110 577L63 514L91 490C114 525 158 571 211 571C266 571 306 541 306 483C306 411 234 371 141 343L151 306C167 311 192 317 219 317C276 317 344 282 344 194C346 102 296 46 227 46C166 46 125 76 99 97C91 104 81 103 71 97C62 90 47 75 46 62C44 50 48 39 62 26C77 10 120 -12 168 -12C242 -12 436 62 436 222Z"></path></g></svg> and (b) brick representation of <span class="nowrap"><svg height="14.0944pt" id="M299" style="vertical-align:-5.341061pt" version="1.1" viewbox="-0.0498162 -8.75334 23.1391 14.0944" width="23.1391pt" 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="M592 498C586 556 582 629 581 675H560C545 656 537 650 510 650H115C87 650 74 652 60 675H40C38 620 33 555 28 495H57C69 539 77 568 89 585C102 607 122 616 205 616H267V123C267 44 259 34 168 28V0H454V28C360 34 352 44 352 123V616H422C498 616 514 608 531 584C542 568 552 543 562 495L592 498Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.917,0)"><path d="M692 302H438V274C537 267 543 260 543 188V103C543 61 531 48 511 37C489 26 458 20 424 20C231 20 146 188 146 333C146 517 258 630 411 630C507 630 582 597 606 474L634 480C627 546 622 601 619 636C586 643 510 665 426 665C230 665 44 552 44 321C44 122 191 -15 411 -15C491 -15 573 7 635 21C629 49 628 81 628 116V202C628 261 632 266 692 274V302Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,18.82,5.233)"><path d="M436 222C436 297 385 359 295 376V378C320 391 343 407 363 428S394 474 394 501C394 578 333 635 239 635C186 635 138 610 110 577L63 514L91 490C114 525 158 571 211 571C266 571 306 541 306 483C306 411 234 371 141 343L151 306C167 311 192 317 219 317C276 317 344 282 344 194C346 102 296 46 227 46C166 46 125 76 99 97C91 104 81 103 71 97C62 90 47 75 46 62C44 50 48 39 62 26C77 10 120 -12 168 -12C242 -12 436 62 436 222Z"></path></g></svg>.</span></div>

Mathematical Problems in Engineering

Total Face Irregularity Strength of Certain Graphs

Figure 5