Study on Eccentric Coloring of a Graph

Huilgol, Medha Itagi (2021) Study on Eccentric Coloring of a Graph. In: Current Topics on Mathematics and Computer Science Vol. 9. B P International, pp. 115-126. ISBN 978-93-91882-90-7

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Abstract

The eccentricity e(u) of a vertex u is the maximum distance of u to any other vertex of G. A vertex v is an eccentric vertex of vertex u if the distance from u to v is equal to e(u). An eccentric coloring of a graph G=(V,E) is a function color: V
N such that

(i) for all u,v
V,(color(u)=color(v))
d(u,v)>color(u).
(ii) for all v
V,color(v)
e(v).

The eccentric chromatic number Xe
N for a graph G is the lowest number of colors for which it is possible to eccentrically color G by colors: V
{1,2,…,Xe }. In this paper, we have considered eccentric colorability of a graph in relation to other properties. we have considered simple undirected graphs without multiple edges and self loops. Also, we have considered the eccentric colorability of lexicographic product of some special class of graphs.

Item Type: Book Section
Subjects: STM Academic > Mathematical Science
Depositing User: Unnamed user with email support@stmacademic.com
Date Deposited: 28 Oct 2023 05:02
Last Modified: 28 Oct 2023 05:02
URI: http://article.researchpromo.com/id/eprint/1555

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