Eccentricity splitting graph of a graph

Abstract

Let G = (V, E) be any connected graph with for all uj , uk ∈ Si if e(uj ) = e(uk )(1 ≤ i ≤ t) with each | Si |≥ 2 and . The eccentricity splitting graph of a graph denoted by ES(G) is obtained by taking a copy of G and adding vertices w 1, w 2, … , wt such that wi is adjacent only to the vertices of Si for 1 ≤ i ≤ t. We initiate the study on eccentricity splitting graph ES(G) and examine its structural properties. We also analyze diameter, girth and chromatic number of eccentricity splitting graphs of certain classes of graphs.