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December 2015 Odd harmonious labeling of some new families of graphs
P. Jeyanthi, S. Philo, Kiki A. Sugeng
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SUT J. Math. 51(2): 181-193 (December 2015). DOI: 10.55937/sut/1454685507

Abstract

A graph G(p,q) is said to be odd harmonious if there exists an injection f:V(G){0,1,2,,2q1} such that the induced function f*:E(G){1,3,,2q1} defined by f*(uv)=f(u)+f(v) is a bijection. A graph that admits odd harmonious labeling is called odd harmonious graph. In this paper, we prove that shadow and splitting of graph K2,n,Cn for n0 (mod 4), the graph Hn,n, double quadrilateral snakes DQ(n),n2, the graph Pr,m if m is odd, banana tree and the path union of cycles Cn for n0 (mod 4) are odd harmonious.

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P. Jeyanthi. S. Philo. Kiki A. Sugeng. "Odd harmonious labeling of some new families of graphs." SUT J. Math. 51 (2) 181 - 193, December 2015. https://doi.org/10.55937/sut/1454685507

Information

Received: 12 April 2015; Revised: 31 October 2015; Published: December 2015
First available in Project Euclid: 8 June 2022

Digital Object Identifier: 10.55937/sut/1454685507

Subjects:
Primary: 05C78

Keywords: double quadrilateral snake , harmonious labeling , odd harmonious labeling , shadow graph , splitting graph

Rights: Copyright © 2015 Tokyo University of Science

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Vol.51 • No. 2 • December 2015
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