On vertex balance index set of some graphs

Adiga, Ch.; Subbaraya, C. K.; Shrikanth, A. S.; Sriraj, M. A.

On vertex balance index set of some graphs

Document Type : Research Paper

Authors

Ch. Adiga ¹

C. K. Subbaraya ²

A. S. Shrikanth ¹

M. A. Sriraj ¹

¹ University of Mysore

² Adichunchanagiri Institute of Technology

Abstract

Let Z2 = {0, 1} and G = (V ,E) be a graph. A labeling f : V → Z2 induces an edge labeling f* : E →Z2 defined by f*(uv) = f(u).f (v). For i ε Z2 let vf (i) = v(i) = card{v ε V : f(v) = i} and ef (i) = e(i) = {e ε E : f*(e) = i}. A labeling f is said to be Vertex-friendly if | v(0) − v(1) |≤ 1. The vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. In this paper we completely determine the vertex balance index set of Kn, Km,n, Cn×P2 and Complete binary tree.

Keywords

Vertex labeling

Vertex-friendly

Vertex balance index set

Subjects