A Novel Construction of Mutually Orthogonal Three Disjoint Union of Certain Trees Squares

Authors

R. El-Shanawany, Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menofia University, Menouf, EgyptFollow
S. Nada, Department of Mathematics, Faculty of Science, Menoufia University, Shebeen Elkom, EgyptFollow
A. Elrokh, Department of Mathematics, Faculty of Science, Menoufia University, Shebeen Elkom, EgyptFollow
E. Sallam, Department of Basic Science, Giza Higher Institute of Engineering and Technology, Giza, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

A family of decompositions {G0,G1,...,Gk−1} of a complete bipartite graph Kn,n is a set of k mutually orthogonal graph squares(MOGS)ifGi andGj areorthogonalforalli,j∈{0,1,...,k−1}andi̸= j.ForanysubgraphGofKn,n withnedges,N(n,G) denotes the maximum number k in a largest possible set {G0,G1,...,Gk−1} of MOGS of Kn,n by G. In this paper we compute some new extensions of the well-known N(n,G) ≥ 3, using a novel approach, where G represents disjoint unions of certain small trees subgraphs of Kn,n.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/170102

Recommended Citation

El-Shanawany, R.; Nada, S.; Elrokh, A.; and Sallam, E. (2023) "A Novel Construction of Mutually Orthogonal Three Disjoint Union of Certain Trees Squares," Applied Mathematics & Information Sciences: Vol. 17: Iss. 1, Article 2.
DOI: http://dx.doi.org/10.18576/amis/170102
Available at: https://digitalcommons.aaru.edu.jo/amis/vol17/iss1/2