A study on coarse deg-centric graphs

Abstract

The coarse deg-centric graph of a simple, connected graph G, denoted by G_cd, is a graph constructed from G such that V(G_cd) = V(G) and E(G_cd) = {v_i v_j : d_G( v_i, v_j) > deg_G(v_i)}. This paper introduces and discusses the concepts of coarse deg-centric graphs and iterated coarse deg-centrication of a graph. It also presents the properties and structural characteristics of coarse deg-centric graphs of some graph families.