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On Mutually Orthogonal Graph-Path Squares
Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf, Egypt
- 1 Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf, Egypt
Open Journal of Discrete Mathematics·Volume 06 (2015)·Pages 7–12·Published 17 December 2015·DOI10.4236/ojdm.2016.61002
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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 ).
KeywordsOrthogonal Graph SquaresOrthogonal Double Cover
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