A New Type of Graphical Passwords Based on Odd-Elegant Labelled Graphs

<div>A So-TOE-graph <svg height="13.2019pt" id="M545" style="vertical-align:-3.515579pt" version="1.1" viewbox="-0.0498162 -9.68632 57.5692 13.2019" width="57.5692pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,.007)"><path d="M1059 256C1059 532 834 755 556 755S53 532 53 256S278 -243 556 -243S1059 -20 1059 256ZM1001 256C1001 8 802 -193 556 -193S111 8 111 256S310 705 556 705S1001 504 1001 256ZM618 256C618 292 591 319 556 319S494 292 494 256C494 219 521 193 556 193S618 219 618 256Z" id="g119-68"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.51,3.466)"><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" id="g50-51"></path></g><g transform="matrix(.013,0,0,-0.013,19.457,0)"><path d="M360 -163L167 270L360 703H298L106 273V267L298 -163H360Z" id="g113-61"></path></g><g transform="matrix(.013,0,0,-0.013,24.826,0)"><path d="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 309 307 360L276 382C223 419 179 455 179 516C179 576 221 632 293 632C379 632 410 564 418 487L448 490C446 536 446 592 449 634Z" id="g113-84"></path></g><g transform="matrix(.0091,0,0,-0.0091,30.897,3.132)"><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" id="g50-50"></path></g><g transform="matrix(.013,0,0,-0.013,35.843,0)"><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" id="g113-45"></path></g><g transform="matrix(.013,0,0,-0.013,40.986,0)"><path d="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 309 307 360L276 382C223 419 179 455 179 516C179 576 221 632 293 632C379 632 410 564 418 487L448 490C446 536 446 592 449 634Z" id="g113-84"></path></g><g transform="matrix(.0091,0,0,-0.0091,47.057,3.132)"><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" id="g50-51"></path></g><g transform="matrix(.013,0,0,-0.013,52.004,0)"><path d="M307 267V273L115 703H53L246 270L53 -163H115L307 267Z" id="g113-63"></path></g></svg> made by the graphs shown in Figure <a href="../fig10/">10</a> for understanding the proof of Case 1 of Theorem <a href="https://static.hindawi.com/articles/scn/volume-2018/9482345/figures/#thm4">8</a>.</div>

Security and Communication Networks

fig11

Figure 11

Figure 11: A New Type of Graphical Passwords Based on Odd-Elegant Labelled Graphs 