| On Orthogonal Certain Disjoint Union of Cycles and Stars Squares |
| Paper ID : 1019-ICEEM2023 (R1) |
| Authors |
|
Zinab Abd El-Lattif Bakr * Department of mathematics, Faculty of science, Tanta University, Tanta, Egypt |
| Abstract |
| A collection G of 2n subgraphs of a complete bipartite graph K_{n,n} of a graph G is called an orthogonal double cover (ODC) such that every edge in the graph K_{n,n} appears one time in two subgraphs in the collection G, and all the subgraphs in G are isomorphic to the graph G. Our goal is to construct two graph squares using a new technique involving two induced starter functions to get an ODC of K_{n,n}. Besides that, from small ingredient ODCs, we can create larger ODCs. Starting with an ODC F of K_{p,p} by pK₂ we replace every point by n new points and every edge by an ODC of K_{n,n} to obtain an ODC of K_{pn,pn} by a certain disjoint union of cycles and stars, where p,n∈ℤ⁺. |
| Keywords |
| Orthogonal double cover,Edge decomposition, Half-starter, Symmetric starter, Orthogonal graph squares. |
| Status: Accepted |