Oral Presentation , Page 136-139 (4)

Volume Title: 2nd IEEE International Conference on Electronic Eng., Faculty of Electronic Eng., Menouf, Egypt, 3-4 July. 2021

Zinab Abd ellatif Bakr

mathematics department, faculty of science, Tanta university, Tanta, Egypt

Let K_{n,n} be a complete bipartite graph on 2n vertices and G be a collection of 2n subgraphs of K_{n,n}, then G is an orthogonal double cover (ODC) of K_{n,n} if every edge of K_{n,n} exists in exactly two members of G and any two members of G share exactly an edge. If all subgraphs in G are isomorphic to a given subgraph G, then G is said to be an ODC of K_{n,n} by G. Our aim is getting an ODC of K_{n,n} by ∪C_{s}; s≤n, and we will make extension for this ODC to get another one of K_{m,m} by ∪(αC_{s}); where m=αn;α∈ℤ⁺.

Orthogonal double cover; half starter; Symmetric starter; symmetric G-square