Bipartite Symmetric Digraph
نویسندگان
چکیده
P2p -factorization of a complete bipartite graph for p, an integer was studied by Wang [1]. Further, Beiling [2] extended the work of Wang[1], and studied the P2k -factorization of complete bipartite multigraphs. For even value of k in Pk -factorization the spectrum problem is completely solved [1, 2, 3]. However for odd value of k i.e. P3 , P5 and P7 , the path factorization have been studied by a number of researchers [4, 5, 6]. Again → P 3 -factorization of complete bipartite symmetric digraph was studied by Beiling [7]. → P 5 -factorization of complete bipartite symmetric digraph was studied by Rajput and Shukla [8]. In the present paper, → P 7 -factorization of complete bipartite symmetric digraph has been studied. It is shown that the necessary and sufficient conditions for the existence of → P 7 -factorization of complete bipartite symmetric digraph are: (1) 4m ≥ 3n, (2) 4n ≥ 3m, (3) m + n ≡ 0(mod7), (4) 7mn/[3(m + n)] is an integer. Mathematics Subject Classification: 68R10, 05C70
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