Elsevier

Discrete Mathematics

Volume 299, Issues 1–3, 28 August 2005, Pages 297-310
Discrete Mathematics

IC-Colorings and IC-Indices of graphs

https://doi.org/10.1016/j.disc.2004.02.026Get rights and content
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Abstract

Given a coloring f:V(G)N of graph G and any subgraph HG we define fs(H)=vV(H)f(v). In particular, we denote fs(G) by S(f). The coloring f is called an IC-coloring if for any integer k[1,S(f)] there is a connected subgraph HG such that fs(H)=k. Also, we define the IC-index of G to beM(G)=max{S(f):f is an IC-coloring of G}.In this paper we examine some well-known classes of graphs and determine their IC-indices. In addition, several conjectures are proposed.

Keywords

IC-coloring
IC-index of a graph

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