Research Article
P h_(4k-1)-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 98 - Issue 11 |
| Published: July 2014 |
| Authors: U S Rajput, Bal Govind Shukla |
10.5120/17231-7559
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U S Rajput, Bal Govind Shukla . P h_(4k-1)-Factorization of Symmetric Complete Bipartite Digraph. International Journal of Computer Applications. 98, 11 (July 2014), 39-43. DOI=10.5120/17231-7559
@article{ 10.5120/17231-7559,
author = { U S Rajput,Bal Govind Shukla },
title = { P h_(4k-1)-Factorization of Symmetric Complete Bipartite Digraph },
journal = { International Journal of Computer Applications },
year = { 2014 },
volume = { 98 },
number = { 11 },
pages = { 39-43 },
doi = { 10.5120/17231-7559 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2014
%A U S Rajput
%A Bal Govind Shukla
%T P h_(4k-1)-Factorization of Symmetric Complete Bipartite Digraph%T
%J International Journal of Computer Applications
%V 98
%N 11
%P 39-43
%R 10.5120/17231-7559
%I Foundation of Computer Science (FCS), NY, USA
Abstract
In path factorization, Ushio K [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 and P_(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 existences 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 ?_(4k-1)-factorization of symmetric complete bipartite digraph of K_(m,n)^*.
References
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- David M. Burton: Elementary Number Theory. UBS Publishers New Delhi, 2004.
- Harary F: Graph theory. Adison Wesley. Massachusettsf complete bipartite symmetric digraph. . IJCA(12845-0234) Volume 73 Number 18 year 2013.
- U. S. Rajput and Bal Govind Shukla: P ?_7-factorization of complete bipartite symmetric digraph. International Mathematical Forum, vol . 6(2011), 1949-1954.
- David M. Burton: Elementary Number Theory. UBS Publishers New Delhi, 2004.
- Harary F: Graph theory. Adison Wesley. Massachusetts, 1972.
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