Super edge local antimagic total labeling of some graph operation

Abstract

Let G be a simple connected, and undirected graph. Graph G has a set of vertex denoted by V(G) and a set of edge denoted by E(G). d(v) is the degree of vertex v ∈ V(G) and Δ(G) is the maximum degree of G. A total labeling of graph G(V, E) is said to be local edge antimagic total labeling if a bijection f : V(G) ∪ E(G) → {1, 2, 3, …, |V(G)| + |E(G)|} such that for any two adjacent edges e 1 and e 2, wt (e 1) ≠ wt (e 2), where for e = uv ∈ G, wt (e) = f(u) + f(uv) + f(v). The local edge antimagic total labeling induces a proper edge coloring of G if each edge e is assigned the color wt (e). The edge local antimagic chromatic number of G denoted by γelat (G), is the minimum number of distinct color induced by edge weights over all local antimagic total labeling of G. In this paper, we determined the edge local antimagic chromatic number of Diamond Ladder graph, Pn ⊙ Pm Three Circular ladder graphht, and shack(F 2, v, n).