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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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References:
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