Regular clique assemblies, configurations, and friendship in Edge-Regular graphs

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Published: Dec 30, 2017
DOI: https://doi.org/10.5556/j.tkjm.48.2017.2237

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Kelly B. Guest
James M. Hammer
Peter D. Johnson
Kenneth J. Roblee

Abstract

An edge-regular graph is a regular graph in which, for some $\lambda$, any two adjacent vertices have exactly $\lambda$ common neighbors. This paper is about the existence and structure of edge-regular graphs with $\lambda =1$ and about edge-regular graphs with $\lambda >1$ which have local neighborhood structure analogous to that of the edge-regular graphs with $\lambda =1$.

Article Details

How to Cite
Guest, K. B., Hammer, J. M., Johnson, P. D., & Roblee, K. J. (2017). Regular clique assemblies, configurations, and friendship in Edge-Regular graphs. Tamkang Journal of Mathematics, 48(4), 301–320. https://doi.org/10.5556/j.tkjm.48.2017.2237
Issue
Vol. 48 No. 4 (2017)
Section
Papers
Author Biographies

Kelly B. Guest

Department of Mathematics, Tuskegee University, Tuskegee, AL 36088, USA

James M. Hammer

Mathematics Department, Cedar Crest College, Allentown, PA 18104, USA.

Peter D. Johnson

Department ofMathematics and Statistics, Auburn University, Auburn, AL 36849-5310, USA

Kenneth J. Roblee

Department ofMathematics and Physics, Troy University, Troy, AL 36082, USA

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