On super (a,1)-edge-antimagic total labelings of cartesian product graphs

Abstract

A graph G(V, E) with order p and size q is called (a,d)-edge-antimagic total if there exists a bijective function f : V(G) ⋃ E(G)→{1, 2, …, p + q} such that the edge-weights λf(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 m (P2□Pn), m (P4□Pn) and m (C4□Pn) for m ≥ 1 and n ≥ 2.