The γ-spectrum of 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 f'(e) = |f(u) - f(v)| for each edge e = uv of G. The value of f is defined as val(f) = X e∈E(G) f'(e) . The-spectrum of a graph G is defined as spec(G) = {val(f) : f is a-labeling of G}. In this paper,-spectrum of cycle with one chord is determined. © 2015 Academic Publications, Ltd.