Odd Harmonious Labeling of Some Classes of Graphs

  • P. Jeyanthi Research Centre, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur - 628 215, Tamil Nadu, India.
  • S. Philo Department of Mathematics, St. Xavier’s College, Palayamkottai, Tirunelveli -627002, Tamilnadu, India.
Keywords: harmonious labeling, odd harmonious labeling, transformed tree, subdivided grid graph, regular bamboo tree

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.

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Published
2020-12-07
How to Cite
[1]
P. Jeyanthi and S. Philo, “Odd Harmonious Labeling of Some Classes of Graphs”, CUBO, A Mathematical Journal, vol. 22, no. 3, pp. 299–314, Dec. 2020.