The γ-spectrum of a graph

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 a labeling f′ : E(G) → {1,2,..., m} of the edges of G defined by f′(e) = |f(u) -f(v)| for each edge e = uv of G. The value of a γ-labeling f is defined as val(f)= Σ f′(e). eεE(G) The γ-spectrum of a graph G is defined as spec(G) = {val(f) : f is a γ-labeling of G}. The γ-spectra of paths, cycles, and complete graphs are determined.