Orthogonal Double Covers of Complete Bipartite Graphs by Certain Disjoint Union Cyclic Graphs

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Published: 2021-11-11

Page: 94-101


R. El-Shanawany

Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf, Egypt.

E. El-Kholy

Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.

T. Homoda

Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.

Z. Bakr *

Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.

*Author to whom correspondence should be addressed.


Abstract

Let kn,n be a complete bipartite graph on 2n vertices and G be a collection of 2n subgraphs of kn,n.G is said to be an orthogonal double cover (ODC) of kn,n if every edge of kn,n is contained in exactly two members of G and any two members share an edge whenever the corresponding vertices are adjacent in kn,n and share no edges whenever the corresponding vertices are non-adjacent in kn,n, and all subgraphs in G are isomorphic to a given subgraph G of kn,n. Our aim in this paper gets an ODC of kn,n by ∪Cs;s≤n, and we construct large (ODCs) of kn,n by ∪(αCs); where m=αn;α∈Z+.

 

Keywords: Graph decomposition, orthogonal double covers, symmetric starter, G-squares


How to Cite

El-Shanawany, R., El-Kholy, E., Homoda, T., & Bakr, Z. (2021). Orthogonal Double Covers of Complete Bipartite Graphs by Certain Disjoint Union Cyclic Graphs. Asian Journal of Pure and Applied Mathematics, 3(1), 94–101. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1335

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