Odd Vertex Equitable Even Labeling of Ladder Graphs

Abstract

Let G be a graph with p vertices and q edges and A={1,3, ...,q} if q is odd or A={1,3, ...,q+1} if q is even. A graph G is said to admit an odd vertex equitable even labeling if there exists a vertex labeling f : V (G) → A that induces an edge labeling f^∗ defined by f^∗(uv) = f(u)+f(v) for all edges uv such that for all a and b in A, |v_f(a)−v_f(b)| ≤ 1 and the induced edge labels are 2,4,...,2q where v_f(a) be the number of vertices v with f(v) = a for a ∈ A. A graph that admits an odd vertex equitable even labeling is called an odd vertex equitable even graph [2]. In this paper we investigate the odd vertex equitable even labeling behavior of some ladder graphs.

Key words and phrases. vertex equitable labeling; vertex equitable graph; odd vertex equitable even labeling, odd vertex equitable even graph.

1991 Mathematics Subject Classification. 05C78