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.
Yang et al. (Tue,) studied this question.