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(P_5)- Factorization of Complete Bipartite Symmetric Digraphs

by U. S. Rajput, Bal Govind Shukla
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 73 - Number 18
Year of Publication: 2013
Authors: U. S. Rajput, Bal Govind Shukla
10.5120/12845-0234

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 },
issue_date = { July 2013 },
volume = { 73 },
number = { 18 },
month = { July },
year = { 2013 },
issn = { 0975-8887 },
pages = { 40-45 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume73/number18/12845-0234/ },
doi = { 10.5120/12845-0234 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:40:38.185050+05:30
%A U. S. Rajput
%A Bal Govind Shukla
%T (P_5)- Factorization of Complete Bipartite Symmetric Digraphs
%J International Journal of Computer Applications
%@ 0975-8887
%V 73
%N 18
%P 40-45
%D 2013
%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
  1. Wang. H, P_2k-factorization of a complete bipartite graph, discrete math. 120 (1993) 307-308.
  2. Du. B. P_3-factorization of complete multi graph. App. math. j. chinese univ. 14B (1999) 122-124.
  3. Ushio K. P_3- factorization of complete bipartite graphs. Discrete math. 72 (1988) 361-366.
  4. Du. B. P_5- factorization of complete bipartite graphs. Discrete math. 308 (2008) 1665 - 1673.
  5. Du. B. P_2k- factorization of complete bipartite multigraph. Austral. j. comb. 21 (2000)197-199.
  6. Harary . F. Graph theory. Adison Wesley. Massachusetts, 1972.
Index Terms

Computer Science
Information Sciences

Keywords

Complete bipartite Graph Factorization of Graph Spanning Graph

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