On Inclusive Local Irregular Vertex Coloring of Shackle Operation Graph

A graph  is an ordered pair of two sets V and E, written .  is the set of vertices and  is the set of edges of the graph . The labeling of the graph is defined by  where  is the labeling of the vertices. The function  is the vertex coloring of the inclusive local irregularity if . The minimum color of the inclusive local irregularity vertex coloring is called the inclusive local irregularity chromatic number. This article will discuss the coloring of inclusive local irregularities on the graph resulting from the vertex shackle operation.