On Super Local Antimagic Total Edge Coloring of Some Wheel Related Graphs

Abstract

Let G be a connected graph, let V(G) be the vertex set of graph G, and let E(G) be the edge set of graph G. Thus, the bijective function f : V(G) ∪ E(G) −→ {1, 2, 3, ..., |V(G)| + |E(G)|} is called a local antimagic total edge labeling if for two adjacent edges e 1 and e 2 , w t (e 1 ) w t (e 2 ), where for e = uv ∈ G, w (e) = f (u) + f (v) + f (uv). Thus, the local antimagic total edge labeling by induces a proper edge coloring of a graph G if each edge e is assigned the color w t (e). The local antimagic total edge coloring, denoted by γ leat t (G) is the minimum number of colors taken over all colorings induced by local antimagic total edge labelings of a graph G. In this research, we determine the local super antimagic total edge coloring of some wheel related graph including fan, wheel, gear and friendship graph.