The THE LOCAL ANTIMAGIC TOTAL CHROMATIC NUMBERS ON BARBELL WHEEL GRAPHS - Sugeng, Kiki A; M. Fachriza, Evan (Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang, 2025)
Abstract. % Dalam bahasa Inggris Let G=(V,e) be a graph with a finite non-empty vertex set V(G) and a edge set E(G). A local antimagic total labeling on graph G defined as a bijective mapping f from a union of the vertex set and the edges set of G to a set of integers {1,2,…,|V(G)|+|E(G)|} such as for all two adjacent vertices u and v we have w_t(u)≠ w_t(v), where w_t(u)=f(u)+_eE(u)f(e) is a weight of vertex u, and E(u) is a set of adjacent edges on the vertex u. Each distinct vertex weight in local antimagic total labeling can be considered as distinct colors, so that local antimagic total labeling on graph G induces vertex coloring on graph G, with minimum numbers of colors or its chromatic number denoted as χ_lat(G). The barbell wheel graph BW_n,k, with n≥3 and k≥2, is defined as a graph with two subgraphs of wheels W_n that are connected by the path subgraph P_k at each center vertex. In this paper, we prove that the barbell wheel graph BW_n,k has local antimagic total labeling. We also determine its local antimagic total chromatic number.