On the Inclusive Local Irregularity Vertex Coloring of Centripetal Graph Families

Abstract

A graph $G$ is an ordered pair of sets denoted by $G=(V,E)$ where $V(G)$ is the vertex set and $E(G)$ is the edge set. Graph coloring requires that all vertices be colored using as few colors as possible such that no two adjacent vertices share the same color. One extension of graph coloring is the inclusive local irregular vertex coloring, which is a coloring that also takes into account the label of each vertex itself. The number of distinct colors obtained is called the inclusive local irregular chromatic number, denoted by $\chi_{lis}^i(G)$. This research presents five new theorems related to inclusive local irregular vertex coloring of centripetal graph families, namely the octopus graph $(O_{n})$, sandat graph $(St_{n})$, butterfly graph $(BF_{m,n})$, tunjung graph $(Tj_{n})$, and the sunflower graph $(Sf_{n})$.