PEWARNAAN TITIK KETAKTERATURAN LOKAL INKLUSIF PADA KELUARGA GRAF BICYCLIC

Abstract

Graph G is an ordered pair of a set of vertices V(G) and a set of edges E(G), which are unordered pairs of vertices. Graphs represent relationships among objects. A key topic is graph coloring, including vertex, edge, and region coloring. One development is inclusive local irregularity vertex coloring, which is labeling vertices such that the weight of a vertex, obtained from the sum of the vertex's own label and its neighbors' labels, is different from the weights of its neighbors' labels. The minimum number of colors is called the inclusive local irregular chromatic number, \chi_{lis_i}(G). This study aims to determine coloring results and the inclusive local irregular chromatic number for bicyclic graph families, including type I B1_(n, m), type II B2_(n, m, r), and type III B3_(n, m, t). The research uses axiomatic deductive and pattern recognition methods. The results provide a new theorem and are expected to serve as a foundational study contributing to graph theory development