Super edge-antimagic labelings of the generalized Petersen graph P(n, (n - 1)/2)

Abstract

An (a, d)-edge-antimagic total labeling of G is a one-to-one mapping f taking the vertices and edges onto 1, 2,..., |V(G)| + |E(G)| so that the edge-weights w(xy) = f(x) + f(y) + f(xy), xy ∈ E(G), form an arithmetic progression with initial term a and common difference d. An (a, d)-edge-antimagic total labeling is called super (a, d)-edge-antimagic total if f(V(G)) = {1, 2,..., |V(G)|}. This paper considers such labelings applied to cycles and generalized Petersen graphs.