TITLE:
On Mutually Orthogonal Graph-Path Squares
AUTHORS:
Ramadan El-Shanawany
KEYWORDS:
Orthogonal Graph Squares, Orthogonal Double Cover
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.6 No.1,
December
17,
2015
ABSTRACT: A decomposition of a graph H is a partition of the edge set of H into edge-disjoint subgraphs . If for all , then G is a decomposition of H by G.
Two decompositions and of the complete
bipartite graph are orthogonal if, for all . A set of decompositions of is a set of k mutually orthogonal graph squares (MOGS) if and are orthogonal for all and . For any bipartite graph G with n edges, denotes the maximum number k in a largest possible set of MOGS of by G. Our objective in this
paper is to compute where is a path of length d with d + 1 vertices (i.e. Every edge of this path is one-to-one corresponding to an
isomorphic to a certain graph F).