International Journal of Academic and Applied Research (IJAAR)   Year: 2021 | Volume: 5 | Issue: 8 | Page No.: 13-17 On Local Irregularity Vertex Coloring of Tree Graph Family Syahril Maghfiro, Dafik, Robiatul Adawiyah, Arika Indah Kristiana, Rafiantika Megahnia Prihandini Abstract: The graph G is a pair of finite sets (V,E) where V is the set of vertex and E is the set of edge. A graph G is called local irregularity vertex coloring if there is a function l: V(G)? {1,2,...,k} is label function and weight function w: V(G) ? N is desined as w(u)=?_(v?N(u))?l(v) . The function w is called local irregularity vertex coloring if: (i) opt(l)=min?{maks(l_i );l_i is label function}, (ii) for every uv?E(G),w(u)?w(v). The chromatic number of local irregularity vertex coloring denoted by ?_lis (G) is defined as ?_lis (G)=min?{|w(V(G))|;w local irregularity vertex coloring}. In this paper, we will learn about local irregularity vertex coloring of tree graph family. All graph in this paper are member of tree graph family, namely double star graph, caterpillar graph, double broom graph, and banana tree graph.