Two-disjoint-cycle-cover vertex pancyclicity of split-star networks

Chang Liu; Ruichao Niu; Yuefeng Yang

paper

Two-disjoint-cycle-cover vertex pancyclicity of split-star networks

arXiv:2605.28082

Abstract

Let $r_{1}$ and $r_{2}$ be positive integers with $r_{1} \leq r_{2}$ . A graph $G$ is called $2$ -DCC vertex $[r_{1}, r_{2}]$ -pancyclic if, for any two distinct vertices of $G$ and any integer $ℓ \in [r_{1}, r_{2}]$ , there exist two vertex-disjoint cycles of lengths $ℓ$ and $∣ V (G) ∣ - ℓ$ , respectively, containing the two vertices separately. In this paper, we investigate the two-disjoint-cycle-cover vertex pancyclicity of the split-star network $S_{n}^{2}$ . We prove that $S_{n}^{2}$ is $2$ -DCC vertex $[3, n! /2]$ -pancyclic for $n \geq 4$ .