%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