γ-Labeling of a cycle with one chord

Abstract

Let G be a graph of order n and size m. A γ-labeling of G is a one-to-one function f: V (G) → {0, 1, 2, …, m} that induces an edge-labeling f':E(G) → {1,2,…,M on G defined by(Formula presented) In this paper, we determine the maximum and minimum values of a γ-labeling of a graph derived from cycle with adding one chord. © Springer International Publishing AG 2016.