Research Article
(P_5)- Factorization of Complete Bipartite Symmetric Digraphs
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
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| Volume 73 - Issue 18 |
| Published: July 2013 |
| Authors: U. S. Rajput, Bal Govind Shukla |
10.5120/12845-0234
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U. S. Rajput, Bal Govind Shukla . (P_5)- Factorization of Complete Bipartite Symmetric Digraphs. International Journal of Computer Applications. 73, 18 (July 2013), 40-45. DOI=10.5120/12845-0234
@article{ 10.5120/12845-0234,
author = { U. S. Rajput,Bal Govind Shukla },
title = { (P_5)- Factorization of Complete Bipartite Symmetric Digraphs },
journal = { International Journal of Computer Applications },
year = { 2013 },
volume = { 73 },
number = { 18 },
pages = { 40-45 },
doi = { 10.5120/12845-0234 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2013
%A U. S. Rajput
%A Bal Govind Shukla
%T (P_5)- Factorization of Complete Bipartite Symmetric Digraphs%T
%J International Journal of Computer Applications
%V 73
%N 18
%P 40-45
%R 10.5120/12845-0234
%I Foundation of Computer Science (FCS), NY, USA
Abstract
In path factorization, H. Wang [1] gives the necessary and sufficient conditions for the existence of P_k-factorization of a complete bipartite graph for k, an even integer. Further, Beiling Du [2] extended the work of H. Wang, and studied the P_2k-factorization of complete bipartite multigraph. For odd value of k the work on factorization was done by a number of researchers. P_3-factorization of complete bipartite graph was studied by K. Ushio [3]. P_5-factorization of complete bipartite graph was studied by J. Wang [4]. In the present paper, we study (P_5 ) ?-factorization of complete bipartite symmetric digraphs and show that the necessary and sufficient conditions for the existence of (P_5 ) ?-factorization of complete bipartite symmetric digraphs are: (1)3m?2n, (2) 3n?2m, (3)m+n?0(mod 5) and (4)5mn/2(m+n) is an integer. Mathematics Subject Classification 68R10, 05C70, 05C38.
References
- Wang. H, P_2k-factorization of a complete bipartite graph, discrete math. 120 (1993) 307-308.
- Du. B. P_3-factorization of complete multi graph. App. math. j. chinese univ. 14B (1999) 122-124.
- Ushio K. P_3- factorization of complete bipartite graphs. Discrete math. 72 (1988) 361-366.
- Du. B. P_5- factorization of complete bipartite graphs. Discrete math. 308 (2008) 1665 - 1673.
- Du. B. P_2k- factorization of complete bipartite multigraph. Austral. j. comb. 21 (2000)197-199.
- Harary . F. Graph theory. Adison Wesley. Massachusetts, 1972.
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