%0 Journal Article %T On Mutually Orthogonal Graph-Path Squares %A Ramadan El-Shanawany %J Open Journal of Discrete Mathematics %P 7-12 %@ 2161-7643 %D 2016 %I Scientific Research Publishing %R 10.4236/ojdm.2016.61002 %X

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 %K Orthogonal Graph Squares %K Orthogonal Double Cover %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=61973