On super (a, l)-edge-antimagic total labelings of subdivision of stars

Abstract

A graph G(V, E) with order p and size q is called (a,d)-edge-antimagic total labeling graph if there exists a bijective function f : V(G)∪E(G) → {1,2, ...,p+q} such that the edge-weights λ _f(uv) = f(u)+f(v)+f(uv),uv⋯ E(G), form an arithmetic sequence with first term a and common difference d. Such a labeling is called super if the p smallest possible labels appear at the vertices. In this paper, we study super (a, 1)-edge-antimagic properties of l(S _n ^m) for positive integers l, m and n.