A STUDY OF THE NEUTROSOPHIC DOMINATING PATH-COLORING NUMBER AND MULTIVALUED STAR CHROMATIC NUMBER IN NEUTROSOPHIC GRAPHS

Abstract

Graph products are introduced to obtain information on large graphs from similar information on smaller graphs. This paper introduces a new way to study the dominant path-coloring number and neutrosophic dominating path-coloring number in neutrosophic graphs. It also proposes a new method for multivalued star coloring on the corona product of two neutrosophic graphs and calculates the multivalued star chromatic number of these graphs. The neutrosophic dominating path-coloring number can be used as a measure of connectivity in neutrosophic graphs. Here, multivalued star chromatic number of a neutrosophic graph can be used to determine the number of colors needed to color the vertices of the graph so that no two adjacent vertices have the same color.  The edge corona product of a star graph with a path graph, cycle graph, complete graph, or any simple graph also has the same property. Theorems are derived for multivalued star coloring on the corona product in neutrosophic graphs and provides examples.