Pewarnaan Titik Ketakteraturan Lokal Inklusif pada Hasil Operasi Comb Graf Kipas

Abstract

Graph theory is a branch of mathematics used to model discrete objects through the representation of vertices and edges. One concept that has developed in graph theory is graph coloring, which is the assignment of colors to the vertices of a graph such that any two adjacent vertices have different colors. A development of this concept is inclusive local irregular vertex coloring, which is the assignment of labels to each vertex in a graph under certain rules so that the resulting vertex weights are different for adjacent vertices. This research aims to determine the minimum value of inclusive local irregular vertex coloring on graphs resulting from the comb operation. The comb operation forms a new graph by connecting the central vertex of a copy of graph 𝐻 to every vertex of graph 𝐺. This study discusses Inclusive Local Irregular Vertex Coloring on the Comb Operation of Fan Graphs, namely the star graph comb fan graph, complete bipartite graph comb fan graph, fan graph comb fan graph, and ladder graph comb fan graph. The type of research used is exploratory with an axiomatic deductive method and pattern recognition. The results of this study obtain new theorems regarding the inclusive local irregular chromatic number for each graph studied.