Malaysian Journal of Mathematical Sciences, May 2018, Vol. 12, No. 2
On Orthogonal Labelling for the Orthogonal Covering of the Circulant Graphs
El-Shanawany, R. and El-Mesady, A.
Corresponding Email: ramadan_elshanawany380@yahoo.com
Received date: 27 April 2016
Accepted date: 16 May 2018
Abstract:
If we have two Abelian groups, then we can use the cartesian product of these two groups for labelling the circulants and this manages us to
find the cyclic orthogonal double covers (CODCs) of these circulants by certain infinite graph classes, such as \(K_{1,2m-2}\cup K_{1,2m(n-1)}, K_{1,4(n-1)}\cup K_{1,4(m-1)}\cup K_{1,4(m-1)(n-1)}\) with \(m\) and \(n > 1\), and by other certain defined graphs in this paper.
Keywords: Circulant graph, Orthogonal double cover, Orthogonal labelling
