20.500.12556/RUL-168563 Sharp lower bounds on the metric dimension of circulant graphs For $n \ge 2t+1$ where $t \ge 1$, the circulant graph $C_n (1, 2, \dots , t)$ consists of the vertices $v_0, v_1, v_2, \dots , v_{n-1}$ and the edges $v_i v_{i+1}$, $v_i v_{i+2}, \dots , v_i v_{i + t}$, where $i = 0, 1, 2, \dots , n-1$, and the subscripts are taken modulo $n$. We prove that the metric dimension ${\rm dim} (C_n (1, 2, \dots , t)) \ge \left\lceil \frac{2t}{3} \right\rceil + 1$ for $t \ge 5$, where the equality holds if and only if $t = 5$ and $n = 13$. Thus ${\rm dim} (C_n (1, 2, \dots , t)) \ge \left\lceil \frac{2t}{3} \right\rceil + 2$ for $t \ge 6$. This bound is sharp for every $t \ge 6$. Cayley graph distance resolving set Cayleyev graf razdalja true false true Angleški jezik Slovenski jezik Članek v reviji 2025-04-17 09:32:43 2025-04-17 09:32:44 2025-04-18 04:34:09 0000-00-00 00:00:00 2025 0 0 Str. 79-98 no. 1 Vol. 10 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-01-01 519.17 2538-2128 10.22049/cco.2023.28792.1725 232767747 CCO_Volume_10_Issue_1_Pages_79-98_(1).pdf CCO_Volume_10_Issue_1_Pages_79-98_(1).pdf 1 67B7CE233CF7DAA01551B01F028BD3B2 3bf74e2aa7cc1bac51fc03dd5e662b37749751fc47f0fbdcbfa826d2e68902d1 27be37a8-1b5f-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=208627 https://comb-opt.azaruniv.ac.ir/article_14679.html 1 07aa2819-1b5d-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=208625 Fakulteta za matematiko in fiziko 0 0 0