Pancyclicity in the Cartesian Product $(K_9-C_9{)}^n$

Abstract

A graph $G$ on $m$ vertices is pancyclic if it contains cycles of length $l$, $3\le l\le m$ as subgraphs in $G$. The complete graph $K_9$ on 9 vertices with a cycle $C_9$ of length 9 deleted from $K_9$ is denoted by $(K_9-C_9)$. In this paper, we prove that $(K_9-C_9{)}^n$, the Cartesian product of $(K_9-C_9)$ taken $n$ times, is pancyclic.

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