Research Article
P9-factorization of Symmetric Complete Bipartite Digraph
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
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| Volume 66 - Issue 17 |
| Published: March 2013 |
| Authors: U S Rajput, Bal Govind Shukla |
10.5120/11175-6199
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U S Rajput, Bal Govind Shukla . P9-factorization of Symmetric Complete Bipartite Digraph. International Journal of Computer Applications. 66, 17 (March 2013), 14-21. DOI=10.5120/11175-6199
@article{ 10.5120/11175-6199,
author = { U S Rajput,Bal Govind Shukla },
title = { P9-factorization of Symmetric Complete Bipartite Digraph },
journal = { International Journal of Computer Applications },
year = { 2013 },
volume = { 66 },
number = { 17 },
pages = { 14-21 },
doi = { 10.5120/11175-6199 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2013
%A U S Rajput
%A Bal Govind Shukla
%T P9-factorization of Symmetric Complete Bipartite Digraph%T
%J International Journal of Computer Applications
%V 66
%N 17
%P 14-21
%R 10.5120/11175-6199
%I Foundation of Computer Science (FCS), NY, USA
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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- U. S. Rajput and Bal Govind Shukla: (P_5 ) ?-factorization of complete bipartite symmetric digraph. National Seminar on "Current Trends in Mathematics with Special Focus on O. R. and Computers", D. R. M. L. A. U. Faizabad, India, (2010).
- U. S. Rajput and Bal Govind Shukla: (P_7 ) ?-factorization of complete bipartite symmetric digraph. International Mathematical Forum, vol. 6(2011), 1949-1954.
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