On Super Edge Local Antimagic Total Labeling by Using an Edge Antimagic Vertex Labeling Technique

Abstract

In this paper, we consider that all graphs are finite, simple and connected. Let G(V,E) be a graph of vertex set V and edge set E. By a edge local antimagic total labeling, we mean a bijection f:V(G)∪E(G)→{1,2,3,...,|V(G)|+|E(G)|} satisfying that for any two adjacent edges e_1 and e_2, w_t (e_1)≠w_t (e_2), where for e=uv∈G,w_t (e)=f(u)+f(v)+f(uv). Thus, any edge local antimagic total labeling induces a proper edge coloring of G if each edge e is assigned the color w_t (e). It is considered to be a super edge local antimagic total coloring, if the smallest labels appear in the vertices. The chromatic number of super edge local antimagic total, denoted by γ_leat (G), is the minimum number of colors taken over all colorings induced by super edge local antimagic total labelings of G. In this paper, we investigate the lower bound of super edge local antimagic total coloring of graphs and the existence the chromatic number of super edge local antimagic total labeling of ladder graph L_n, caterpillar graph C_(n,m), and graph coronations P_n⨀P_2 and C_n⨀P_2..