Affiliation:
1. College of Information Technology, Anhui Vocational College of Defense Technology, Luan 237011, China
2. Department of Mathematics, COMSATS University Islamabad, Sahiwal 57000, Pakistan
Abstract
The advancement in coloring schemes of graphs is expanding over time to solve emerging problems. Recently, a new form of coloring, namely P3-coloring, was introduced. A simple graph is called a P3-colorable graph if its vertices can be colored so that all the vertices in each P3 path of the graph have different colors; this is called the P3-coloring of the graph. The minimum number of colors required to form a P3-coloring of a graph is called the P3-chromatic number of the graph. The aim of this article is to determine the P3-chromatic number of different well-known classes of bipartite graphs such as complete bipartite graphs, tree graphs, grid graphs, and some special types of bipartite graphs. Moreover, we have also presented some algorithms to produce a P3-coloring of these classes with a minimum number of colors required.
Funder
National Key R& D Program Fund Project
Anhui Provincial University Natural Science Research Major Project
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
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