Degree affinity number of certain 2 -regular graphs

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 , … , 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.