A Study on Regular Domination in Vague Graphs with Application

<div><span class="nowrap"><svg height="12.4698pt" id="M182" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 55.0367 12.4698" width="55.0367pt" 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="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,-0.013,4.498,0)"><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,-0.013,8.996,0)"><path d="M401 397C401 420 368 448 302 448C245 448 169 416 122 377C62 327 23 254 23 169C23 45 83 -12 181 -12C252 -12 323 29 374 85L358 107C305 62 257 43 210 43C147 43 110 98 110 189V214L313 208L321 256L115 250C132 342 190 405 253 405C291 405 323 389 346 360C356 348 364 348 377 357C392 367 401 384 401 397Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.183,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g><g transform="matrix(.013,0,0,-0.013,19.129,0)"><path 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"></path></g><g transform="matrix(.013,0,0,-0.013,24.273,0)"><path d="M401 397C401 420 368 448 302 448C245 448 169 416 122 377C62 327 23 254 23 169C23 45 83 -12 181 -12C252 -12 323 29 374 85L358 107C305 62 257 43 210 43C147 43 110 98 110 189V214L313 208L321 256L115 250C132 342 190 405 253 405C291 405 323 389 346 360C356 348 364 348 377 357C392 367 401 384 401 397Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,29.46,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g><g transform="matrix(.013,0,0,-0.013,34.406,0)"><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><g transform="matrix(.013,0,0,-0.013,38.904,0)"><path 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"></path></g><g transform="matrix(.013,0,0,-0.013,44.047,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g><g transform="matrix(.013,0,0,-0.013,50.287,0)"><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>-</span>Regular VWDS of VG.</div>

Advances in Mathematical Physics

A Study on Regular Domination in Vague Graphs with Application

Figure 3