Degree affinity number of certain \(2\)-regular graphs

Author(s): Johan Kok1
1Independent Mathematics Researcher, City of Tshwane, South Africa & Visiting Faculty at CHRIST (Deemed to be a University), Bangalore, India.
Copyright © Johan Kok. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper furthers the study on a new graph parameter called the degree affinity number. The degree affinity number of a graph \(G\) is obtained by iteratively constructing graphs, \(G_1,G_2,\dots,G_k\) of increased size by adding a maximal number of edges between distinct pairs of distinct vertices of equal degree. Preliminary results for certain \(2\)-regular graphs are presented.

Keywords: Degree affinity edge, degree affinity number.