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P9-factorization of Symmetric Complete Bipartite Digraph

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International Journal of Computer Applications
© 2013 by IJCA Journal
Volume 66 - Number 17
Year of Publication: 2013
Authors:
U S Rajput
Bal Govind Shukla
10.5120/11175-6199

U S Rajput and Bal Govind Shukla. Article: P9-factorization of Symmetric Complete Bipartite Digraph. International Journal of Computer Applications 66(17):14-21, March 2013. Full text available. BibTeX

@article{key:article,
	author = {U S Rajput and Bal Govind Shukla},
	title = {Article: P9-factorization of Symmetric Complete Bipartite Digraph},
	journal = {International Journal of Computer Applications},
	year = {2013},
	volume = {66},
	number = {17},
	pages = {14-21},
	month = {March},
	note = {Full text available}
}

Abstract

In path factorization, Ushio [1] gave the necessary and sufficient conditions for P_k-design when k is odd. P_2p -factorization of a complete bipartite graph for p an integer, was studied by Wang [2]. Further, Beiling [3] extended the work of Wang [2], and studied P_2k -factorization of complete bipartite multigraphs. For even value of k in P_k-factorization the spectrum problem is completely solved [1, 2, 3]. However, for odd value of k i. e. P_3,P_5,P_7,P_9 andP_(4k-1), the path factorization have been studied by a number of researchers [4, 5, 6, 7, 8]. The necessary and sufficient conditions for the existence of? P ??_3-factorization of symmetric complete bipartite digraph were given by Du B [9]. Earlier we have discussed the necessary and sufficient conditions for the existence of P ?_5 and P ?_7 -factorization of symmetric complete bipartite digraph [10, 11]. Now, in the present paper, we give the necessary and sufficient conditions for the existence of P ?_9-factorization of symmetric complete bipartite digraph, K_(m,n)^*.

References

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