The chromatic number of local antimagic total edge coloring of some related cycle graphs

Abstract

A graph G = (V, E) be connected, finite, and undirected graph without multiple edges and loops. Graph G(V, E) consists two sets of vertices V and edge E. A graph called related cycle if the subgraph of graph G contains a cycle. Local antimagic total edge labeling is defined a bijection f : V ∪ E → {1, 2, 3, …, |V | + |E|}, if for any two adjacent edges e1 and e2, wt(e1) ≠ wt(e2), where for e = ab ∈ G, wt(e) = f(a) + f(ab) + f(b). Thus, the local antimagic total edge labeling induces a proper edge coloring of G if each edge e is assigned the color wt(e). The local antimagic total edge chromatic number of G denoted by γlate(G), is the minimum of colors needed to coloring the edges of a graph, the number of distinct induced edge labels over all local antimagic total labeling of G. In this paper we study the local antimagic total edge coloring of some related cycle of graphs and determined the chromatic number of some related cycle graphs namely triangular book Btr, prism graph Pr, sun graph Mr and kite graph Kr, s.