Abstract
Let is a simple and connected graph with as vertex set and as edge set. Vertex labeling on inclusive local irregularity vertex coloring is defined by mapping and the function of the inclusive local irregularity vertex coloring is with . In other words, an inclusive local irregularity vertex coloring is defined by coloring the graph so that its weight value is obtained by adding up the labels of the neighboring vertex and its label. The inclusive local irregularity chromatic number is defined as the minimum number of colors obtained from coloring the vertex of the inclusive local irregularity in graph G, denoted by . In this paper, we learn about the inclusive local irregularity vertex coloring and determine the chromatic number on the book graphs.
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