Irreversible <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2723999pt" id="M1" height="12.533pt" version="1.1" viewBox="-0.0657574 -12.2606 8.79534 12.533" width="8.79534pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-108" d="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z"/></g></svg>-</span>Threshold Conversion Number of Circulant Graphs

<div>An I3CS of 11 vertices on <span class="nowrap"><svg height="12.5794pt" id="M903" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 53.9123 12.5794" width="53.9123pt" 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="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.619,3.132)"><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(.0091,0,0,-0.0091,13.051,3.132)"><path d="M253 635C142 635 71 555 71 471C71 401 113 353 178 316C144 294 106 267 91 252C70 231 46 202 46 157C46 51 132 -12 241 -12C328 -12 442 52 442 168C442 257 379 305 311 343C354 373 380 398 388 407C406 428 417 458 417 487C417 568 348 635 253 635ZM240 600C288 600 340 563 340 481C340 423 313 387 279 360C207 394 148 427 148 499C148 549 182 600 240 600ZM252 23C188 23 129 73 129 163C129 217 162 266 211 298C289 260 360 217 360 144C360 69 312 23 252 23Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.014,0)"><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,-0.013,22.512,0)"><path d="M293 -169V-141C218 -131 209 -90 209 -44C209 19 222 85 222 152C222 207 198 255 139 269V273C199 286 222 334 222 388C222 454 209 523 209 588C209 632 218 671 293 681V709C234 709 148 695 148 577C147 513 155 438 155 372C155 337 152 291 64 285V256C152 250 155 204 155 169C156 105 148 31 148 -41C148 -157 234 -169 293 -169Z"></path></g><g transform="matrix(.013,0,0,-0.013,27.023,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,33.263,0)"><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,-0.013,38.406,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z"></path></g><g transform="matrix(.013,0,0,-0.013,44.646,0)"><path d="M283 255V284C195 290 192 337 192 375C192 436 200 508 200 580C200 696 116 709 54 709V681C127 671 139 634 139 588C138 524 125 452 125 387C125 333 149 286 209 272V268C148 253 125 206 125 151C126 87 139 16 139 -47C139 -92 127 -131 54 -141V-169C115 -169 200 -152 200 -41C200 32 192 104 192 164C192 202 195 249 283 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,49.157,0)"><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></div>

Journal of Applied Mathematics

fig7

Figure 7

Figure 7: Irreversible <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2723999pt" id="M1" height="12.533pt" version="1.1" viewBox="-0.0657574 -12.2606 8.79534 12.533" width="8.79534pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-108" d="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z"/></g></svg>-</span>Threshold Conversion Number of Circulant Graphs 

Journal of Applied Mathematics

Irreversible -Threshold Conversion Number of Circulant Graphs

Figure 7