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 $f: V(G)\rightarrow\left\{0, 1, 2,\cdots,2q-1\right\}$ such that the induced function $f^{*}: E(G)\rightarrow\left\{1, 3,\cdots,2q-1\right\}$ defined by $f^{*}(uv) = f(u)+ f(v)$ is a bijection. In this paper we prove that $T_p$- tree, $T\hat\circ P_m$, $T\hat\circ 2P_m$, regular bamboo tree, $C_n\hat\circ P_m$, $C_n\hat\circ 2P_m$ and subdivided grid graphs are odd harmonious.

Keywords

• harmonious labeling
• odd harmonious labeling
• transformed tree
• subdivided grid graph
• regular bamboo tree