Girth tenacity of some cube-like networks.
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| Title: | Girth tenacity of some cube-like networks. |
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| Authors: | Yang, Yuxing1 (AUTHOR) yyx@htu.edu.cn, Li, Jing1,2 (AUTHOR) jing-li83@hotmail.com, Zhao, Shu-Li1 (AUTHOR) |
| Source: | Discrete Applied Mathematics. Oct2026, Vol. 391, p114-121. 8p. |
| Subjects: | Graph theory, Hypercubes, Hypercube networks (Computer networks) |
| Abstract: | The girth vertex (resp. edge) tenacity g τ v (G) (resp. g τ e (G)) of a non-acyclic simple graph G is defined to be the maximum number k such that the removal of any k vertices (resp. edges) of G does not change its girth. In this paper, we mainly investigated the girth tenacity of the exchanged hypercube E H (s , t) with s , t ≥ 1 , the ternary n -cube Q n 3 and the exchanged ternary n -cube E 3 C (r , s , t) with n = r + s + t and r , s , t ≥ 0. We proved that (i) g τ v (E H (1 , 1)) = 0 , g τ v (E H (s , t)) = 2 ⌊ 2 t + 1 3 ⌋ − 1 for s = 1 and t ≥ 2 , g τ v (E H (s , t)) = 2 ⌊ 2 s + 1 3 ⌋ − 1 for t = 1 and s ≥ 2 , g τ v (E H (s , t)) = ⌊ 2 t + 1 3 ⌋ 2 s + ⌊ 2 s + 1 3 ⌋ 2 t − 1 for min { s , t } ≥ 2 , and (i i) g τ v (Q n 3) = 3 n − 1 − 1 , g τ e (Q n 3) = n 3 n − 1 − 1 , and (i i i) g τ v (E 3 C (r , s , t)) = 3 n − 1 − 1 , g τ e (E 3 C (r , s , t)) = (n + 2) 3 n − 2 − 1. Some results on the girth tenacity of the hypercube were also listed. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
| Abstract: | The girth vertex (resp. edge) tenacity g τ v (G) (resp. g τ e (G)) of a non-acyclic simple graph G is defined to be the maximum number k such that the removal of any k vertices (resp. edges) of G does not change its girth. In this paper, we mainly investigated the girth tenacity of the exchanged hypercube E H (s , t) with s , t ≥ 1 , the ternary n -cube Q n 3 and the exchanged ternary n -cube E 3 C (r , s , t) with n = r + s + t and r , s , t ≥ 0. We proved that (i) g τ v (E H (1 , 1)) = 0 , g τ v (E H (s , t)) = 2 ⌊ 2 t + 1 3 ⌋ − 1 for s = 1 and t ≥ 2 , g τ v (E H (s , t)) = 2 ⌊ 2 s + 1 3 ⌋ − 1 for t = 1 and s ≥ 2 , g τ v (E H (s , t)) = ⌊ 2 t + 1 3 ⌋ 2 s + ⌊ 2 s + 1 3 ⌋ 2 t − 1 for min { s , t } ≥ 2 , and (i i) g τ v (Q n 3) = 3 n − 1 − 1 , g τ e (Q n 3) = n 3 n − 1 − 1 , and (i i i) g τ v (E 3 C (r , s , t)) = 3 n − 1 − 1 , g τ e (E 3 C (r , s , t)) = (n + 2) 3 n − 2 − 1. Some results on the girth tenacity of the hypercube were also listed. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 0166218X |
| DOI: | 10.1016/j.dam.2026.04.037 |
