Staff Members - Benha University
New families of odd harmonious graphs
International Journal of Soft Computing, Mathematics and Control (IJSCMC) • 2014
Publication Information
Authors
ME Abdel-Aal
Keywords
Odd harmonious labeling, Eulernian graph, Cartesian product, Cyclic graphs.
Journal
International Journal of Soft Computing, Mathematics and Control (IJSCMC)
Publisher
Not Available
Volume
Vol. 3
Issue
No. 1,
Pages
13
publication.type
International
Paper Link
Open Link
Supplementary Materials
Not Available
Abstract
In this paper, we show that the number of edges for any odd harmonious Eulerian graph is congruent to 0
or 2 (mod 4), and we found a counter example for the inverse of this statement is not true. We also proved
that, the graphs which are constructed by two copies of even cycle Cn sharing a common edge are odd
harmonious. In addition, we obtained an odd harmonious labeling for the graphs which are constructed by
two copies of cycle Cn sharing a common vertex when n is congruent to 0 (mod 4). Moreover, we show
that, the Cartesian product of cycle graph Cm and path Pn for each n ≥ ,2 m ≡ 0 (mod )4 are odd
harmonious graphs. Finally many new families of odd harmonious graphs are introduced.
or 2 (mod 4), and we found a counter example for the inverse of this statement is not true. We also proved
that, the graphs which are constructed by two copies of even cycle Cn sharing a common edge are odd
harmonious. In addition, we obtained an odd harmonious labeling for the graphs which are constructed by
two copies of cycle Cn sharing a common vertex when n is congruent to 0 (mod 4). Moreover, we show
that, the Cartesian product of cycle graph Cm and path Pn for each n ≥ ,2 m ≡ 0 (mod )4 are odd
harmonious graphs. Finally many new families of odd harmonious graphs are introduced.