Eccentric Coloring of Helm Graph, Barbell Graph, Lollipop Graph and Centipede Graph

Abstract

Eccentric coloring is a technique in which higher-numbered colors are used less frequently than
lower-numbered colors. The largest distance between a vertex and all other vertices is known
as its eccentricity. It is denoted by ”e(u)”.If the distance between u and v is equal to e(u), then
vertex v is an eccentric vertex of vertex u. The purpose of this paper is to determine Eccentric
coloring of some simple graphs. For a graph G = (V, E), an Eccentric coloring is a color
function: V → N so that (color(u) = color(v)) ⇒ d(u, v) > color(u) ,∀ u, v ∈ V color(v) ≤ e(v)
,∀ v ∈ V . Is Eccentric coloring of a graph.