Open Journal of Discrete Applied Mathematics
Vol. 3 (2020), Issue 3, pp. 77 – 84
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2020.0046
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2020.0046
Degree affinity number of certain \(2\)-regular graphs
Johan Kok
Independent Mathematics Researcher, City of Tshwane, South Africa & Visiting Faculty at CHRIST (Deemed to be a University), Bangalore, India.; johan.kok@christuniversity.in; Tel.: +27646547285
Copyright © 2020 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.
Received: October 15, 2020 – Accepted: November 20, 2020 – Published: December 14, 2020
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.