Staff Members - Benha University
FURTHER RESULTS ON ODD HARMONIOUS GRAPHS
International Journal on Applications of Graph Theory in Wireless Ad hoc Networks and Sensor Networks (GRAPH-HOC) • 2016
Publication Information
Authors
M.A.Seoud M.E.Abdel-Aal
Keywords
Odd harmonious labeling, m-shadow graph, m-splitting graph.
Journal
International Journal on Applications of Graph Theory in Wireless Ad hoc Networks and Sensor Networks (GRAPH-HOC)
Publisher
Not Available
Volume
8
Issue
3
Pages
14
publication.type
International
Paper Link
Open Link
Supplementary Materials
Not Available
Abstract
In [1] Abdel-Aal has introduced the notions of m-shadow graphs and n-splitting graphs, for all m, n ≥ 1.
In this paper, we prove that, the m-shadow graphs for paths and complete bipartite graphs are odd
harmonious graphs for all m ≥ 1. Also, we prove the n-splitting graphs for paths, stars and symmetric
product between paths and null graphs are odd harmonious graphs for all n≥ 1. In addition, we present
some examples to illustrate the proposed theories. Moreover, we show that some families of graphs admit
odd harmonious libeling.
In this paper, we prove that, the m-shadow graphs for paths and complete bipartite graphs are odd
harmonious graphs for all m ≥ 1. Also, we prove the n-splitting graphs for paths, stars and symmetric
product between paths and null graphs are odd harmonious graphs for all n≥ 1. In addition, we present
some examples to illustrate the proposed theories. Moreover, we show that some families of graphs admit
odd harmonious libeling.