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Extending Vertex and Edge Pancyclic Graphs

  • Megan Cream
  • Ronald J. Gould
  • Kazuhide Hirohata
Original Paper
  • 22 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

  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

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