Local irregular vertex coloring of comb product by path graph and star graph

Let [Formula: see text] be a simple graph and connected. A function [Formula: see text] is called vertex irregular [Formula: see text]-labeling and [Formula: see text] where [Formula: see text] The function of [Formula: see text] is called local irregular vertex coloring if every [Formula: see text] and [Formula: see text] vertex irregular labeling}. The local irregular chromatic number is denoted by [Formula: see text] In this paper, we study local irregular vertex coloring of [Formula: see text], and [Formula: see text]