On the local antimagic total edge chromatic number of amalgamation of graphs

Abstract

A total labeling of simple and connected graph G(V, E) is said to be local antimagic total edge labeling if a bijection f : V(G) ∪ E(G) → {1, 2, 3, …, |V(G)| + |E(G)|}, wt (e1) ≠ wt (e2) for any two adjacent edges e1 and e2, where for e = uv ∈ G, wt (e) = f (u) + f (uv) + f (v). The local antimagic total edge labeling induces a proper edge coloring of G if each edge e is assigned the color wt(e). The minimum number of local antimagic total edge chromatic number of G denoted by γleat(G), is the distinct induced by edge labels over all local antimagic total labeling of G. In this paper we study the existence of local edge antimagic total chromatic number of amalgamation of some special graphs namely amal(Pn, v, m), amal(Cn, v, m),amal(Fn, v, m) and amal(S n, v, m).