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

Abstract

Pancyclicity is a stronger property than Hamiltonicity. In 1973, Bondy stated his celebrated meta-conjecture. Since then, problems related to pancyclicity have attracted a lot of attentions and interests of researchers. A connected graph G is two-disjoint-cycle-cover $[t_1,t_2]$-pancyclic or briefly 2-DCC $[t_1,t_2]$-pancyclic if for any positive integer t with $t\in [t_1,t_2]$, there are two vertex-disjoint cycles $C_1$ and $C_2$ in G satisfying $\left|V\right(C_1\left)\right|=t$ and $\left|V\right(C_2\left)\right|=\left|V\right(G\left)\right|-t$. In this paper, it is proved that the n-dimensional split-star network $S_n^2$ is 2-DCC $[3,\lfloor \frac{n!}{2}\rfloor ]$-pancyclic when $n\ge 3$.