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P9-factorization of Symmetric Complete Bipartite Digraph

by U S Rajput, Bal Govind Shukla
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 66 - Number 17
Year of Publication: 2013
Authors: U S Rajput, Bal Govind Shukla
10.5120/11175-6199

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 },
issue_date = { March 2013 },
volume = { 66 },
number = { 17 },
month = { March },
year = { 2013 },
issn = { 0975-8887 },
pages = { 14-21 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume66/number17/11175-6199/ },
doi = { 10.5120/11175-6199 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:22:39.620647+05:30
%A U S Rajput
%A Bal Govind Shukla
%T P9-factorization of Symmetric Complete Bipartite Digraph
%J International Journal of Computer Applications
%@ 0975-8887
%V 66
%N 17
%P 14-21
%D 2013
%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
  1. Ushio K: G-designs and related designs, Discrete Math. , 116(1993), 299-311.
  2. Wang H:? P?_2p -factorization of a complete bipartite graph, discrete math. 120 (1993) 307-308.
  3. Beiling Du:? P?_2k-factorization of complete bipartite multi graph. Australasian Journal of Combinatorics 21(2000), 197 - 199.
  4. Ushio K: - factorization of complete bipartite graphs. Discrete math. 72 (1988) 361-366.
  5. Wang J and Du B: - factorization of complete bipartite graphs. Discrete math. 308 (2008) 1665 – 1673.
  6. Wang J: - factorization of complete bipartite graphs. Australasian Journal of Combinatorics, volume 33 (2005), 129-137.
  7. U. S. Rajput and Bal Govind Shukla: factorization of complete bipartite graphs. Applied Mathematical Sciences, volume 5(2011), 921- 928.
  8. Du B and Wang J:? P?_(4k-1)-factorization of complete bipartite graphs. Science in China Ser. A Mathematics 48 (2005) 539 – 547.
  9. Du B: (P_3 ) ? - factorization of complete bipartite symmetric digraphs. Australasian Journal of Combinatorics, volume 19 (1999), 275-278.
  10. 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).
  11. U. S. Rajput and Bal Govind Shukla: (P_7 ) ?-factorization of complete bipartite symmetric digraph. International Mathematical Forum, vol. 6(2011), 1949-1954.
  12. David M. Burton: Elementary Number Theory. UBS Publishers New Delhi, 2004.
  13. 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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