Extending Vertex and Edge Pancyclic Graphs
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A graph G of order \(n\ge 3\) 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 \(n\ge 4\) 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.
KeywordsChorded cycle Pancyclic Vertex pancyclic Edge pancyclic
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