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# Extending Vertex and Edge Pancyclic Graphs

• Megan Cream
• Ronald J. Gould
• Kazuhide Hirohata
Original Paper
• 20 Downloads

## Abstract

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.

## Keywords

Chorded cycle Pancyclic Vertex pancyclic Edge pancyclic

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## Copyright information

© Springer Japan KK, part of Springer Nature 2018

## Authors and Affiliations

• Megan Cream
• 1
• Ronald J. Gould
• 2
• Kazuhide Hirohata
• 3
1. 1.Department of MathematicsCedar Crest CollegeAllentownUSA
2. 2.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA
3. 3.Department of Electronic and Computer EngineeringNational Institute of Technology, Ibaraki CollegeIbarakiJapan