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On Mutually Orthogonal Graph-Path Squares

DOI: 10.4236/ojdm.2016.61002, PP. 7-12

Keywords: Orthogonal Graph Squares, Orthogonal Double Cover

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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

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