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arXiv · 2605.28082

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

Chang Liu·Ruichao Niu·Yuefeng Yang
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Abstract

Let $r_1$ and $r_2$ be positive integers with $r_1 \le r_2$. A graph $G$ is called $2$-DCC vertex $[r_1,r_2]$-pancyclic if, for any two distinct vertices of $G$ and any integer $\ell \in [r_1,r_2]$, there exist two vertex-disjoint cycles of lengths $\ell$ and $|V(G)|-\ell$, 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 $n\ge4$.

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Chang Liu, Ruichao Niu, Yuefeng Yang. 2026-05-27. Two-disjoint-cycle-cover vertex pancyclicity of split-star networks. https://arxiv.org/abs/2605.28082

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