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Extending vertex and edge pancyclic graphs. (English) Zbl 1402.05120
Summary: A graph \(G\) of order \(n\geq 3\) is pancyclic if \(G\) contains a cycle of each possible length from 3 to \(n\), and vertex pancyclic (edge pancyclic) if every vertex (edge) is contained on a cycle of each possible length from 3 to \(n\). A chord of a cycle is an edge between two nonadjacent vertices of the cycle, and chorded cycle is a cycle containing at least one chord. We define a graph \(G\) of order \(n\geq 4\) to be chorded pancyclic if \(G\) contains a chorded cycle of each possible length from 4 to \(n\). In this article, we consider extensions of the property of being chorded pancyclic to chorded vertex pancyclic and chorded edge pancyclic.
MSC:
05C38 Paths and cycles
05C12 Distance in graphs
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