id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5353	Shabana, Hanan; El-Shanawany, Ramadan ; Halawa, Sahar 	Orthogonal Decompositions of Regular Graphs and Designing Tree-Hamming Codes	2024	25	.pdf	application/pdf	9768	590	86	Math, 17 (4) (2024), 3492-3516 3493 V (X), E(X) for the vertex set and edge set of the graph X respectively, Pk for a path of k vertices, mG for m disjoint copies of G, and G∪H for disjoint union of graphs G and H. Let G1 = {G1, G2, · · · , Gk} and G2 = {F1, F2, · · · , Fk} be two distinct edge decompositions of H by G such that for each i ∈ {1, 2, · · · k} , Gi ≊ G ≊ Fi. The incidence matrix L = L (s, t) for such ODC G ={Gi a; a ∈ Zn, i ∈ {1, 2}} is a 2n× n2 binary matrix showing the relation between the edges of Kn,n and the the members of G such that every row in L corresponds to a unique graph in G and every column in L corresponds to a unique edge in Kn,n. Let the edge (α0, β1) ∈ E (Kn,n) .	cache/ejpam-5353.pdf	txt/ejpam-5353.txt