Odd Harmonious Labeling of Some Classes of Graphs

Abstract

A graph G ( p, q ) is said to be odd harmonious if there exists an injection f : V ( G ) → { 0 , 1 , 2 , · · · , 2 q − 1 } such that the induced function f ∗ : E ( G ) → { 1 , 3 , · · · , 2 q − 1 } defined by f ∗ ( uv ) = f ( u ) + f ( v ) is a bijection. In this paper we prove that T p - tree, T ˆ ◦ P m , T ˆ ◦ 2 P m , regular bamboo tree, C n ˆ ◦ P m , C n ˆ ◦ 2 P m and subdivided grid graphs are odd harmonious.