Some bounds on local connective Chromatic number

Year 2017, Volume: 5 Issue: 2, 204 - 211, 30.03.2017

Canan Ciftci Pinar Dundar

Abstract

Graph coloring is one of the most
important concept in graph theory. Many practical problems can be formulated as
graph coloring problems. In this paper,
we define a new coloring concept called local connective coloring. A local
connective k-coloring of  a graph G
is a proper vertex coloring, which assigns colors from   {1,2,...,k} to the vertices V(G) in
a such way that any two non–adjacent vertices u and v of a color i
satisfies k(u, v) > i, where k(u, v) is
the maximum number of internally disjoint paths between u  and v. Adjacent vertices are
colored with different colors as in the proper coloring. The smallest integer k
for which there exists a local  connective
k- coloring of G is called the local connective chromatic
number of G, and it is denoted by clc(G).We
study this coloring on  several classes
of graphs and give some general bounds. We also compare local connective
chromatic number of a graph with chromatic 
number and packing chromatic number of it.

Keywords

Graph coloring, packing chromatic number, internally disjoint path

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