Characterization of (Molecular) Graphs with Fractional Metric Dimension as Unity

<div>Resolving neighbourhood sets of <svg height="11.5564pt" id="M531" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 31.6907 11.5564" width="31.6907pt" 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="M622 618V662H20V618H238V0H404V618H622ZM360 44H282V618H360V44Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.851,0)"><path d="M70 662V0H348C544 0 677 137 677 332C677 532 547 662 348 662H70ZM553 541C610 488 633 419 633 342C633 278 609 166 553 126V541ZM509 99C475 62 389 44 342 44H236V618H343C393 618 466 598 509 571V99ZM192 44H114V618H192V44Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.298,0)"><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,-0.013,20.796,0)"><path d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z"></path></g><g transform="matrix(.013,0,0,-0.013,27.036,0)"><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> with minimum cardinality.</div>

Journal of Chemistry

tab4

Table 4

Table 4: Characterization of (Molecular) Graphs with Fractional Metric Dimension as Unity 