On The Packing k-Coloring of Unicyclic Graph Family

Abstract

All graph in this paper is connected graph. Let du,v be a distance between any vertex u and v in graph GV,E. A function c :VG 1, 2, , k is called a packing k  coloring if every two vertex of color i are at least distance i 1. G  p or packing chromatics number of graph G is the smallest integer of k which has packing coloring. Unicyclic graphs are graphs that only have one cycle. This graphs is denoted by Cl , which l is the length of the unicyclic graph. In this paper, we will study about packing k  coloring of graphs and determine their packing chromatic number. We have found the exact values of the packing coloring of unicyclic graph family.