Odd Harmonious Labeling of Some Classes of Graphs
Author
Jeyanthi, P.
Philo, S.
Full text
http://revistas.ufro.cl/ojs/index.php/cubo/article/view/246610.4067/S0719-06462020000300299
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.