On Mutually Orthogonal Graph-Path Squares

Ramadan  El-Shanawany

doi:10.4236/ojdm.2016.61002

Ramadan El-Shanawany^*

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).

Keywords: Orthogonal Graph Squares, Orthogonal Double Cover

Cite this paper: El-Shanawany, R. (2016) On Mutually Orthogonal Graph-Path Squares. Open Journal of Discrete Mathematics, 6, 7-12. doi: 10.4236/ojdm.2016.61002.

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