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P h_(4k-1)-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 98 - Number 11
Year of Publication: 2014
Authors: U S Rajput, Bal Govind Shukla
10.5120/17231-7559

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 },
issue_date = { July 2014 },
volume = { 98 },
number = { 11 },
month = { July },
year = { 2014 },
issn = { 0975-8887 },
pages = { 39-43 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume98/number11/17231-7559/ },
doi = { 10.5120/17231-7559 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:25:58.766825+05:30
%A U S Rajput
%A Bal Govind Shukla
%T P h_(4k-1)-Factorization of Symmetric Complete Bipartite Digraph
%J International Journal of Computer Applications
%@ 0975-8887
%V 98
%N 11
%P 39-43
%D 2014
%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
  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 multigraph. Australasian Journal of Combinatorics 21(2000), 197 - 199.
  4. Ushio K: P_3-factorization of complete bipartite graphs. Discrete math. 72 (1988) 361-366.
  5. Wang J and Du B: P_5-factorization of complete bipartite graphs. Discrete math. 308 (2008) 1665 – 1673.
  6. Wang J : P_7-factorization of complete bipartite graphs. Australasian Journal of Combinatorics, volume 33 (2005), 129-137.
  7. U. S. Rajput and Bal Govind Shukla:P_9-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. . IJCA(12845-0234) Volume 73 Number 18 year 2013.
  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. Massachusettsf complete bipartite symmetric digraph. . IJCA(12845-0234) Volume 73 Number 18 year 2013.
  14. U. S. Rajput and Bal Govind Shukla: P ?_7-factorization of complete bipartite symmetric digraph. International Mathematical Forum, vol . 6(2011), 1949-1954.
  15. David M. Burton: Elementary Number Theory. UBS Publishers New Delhi, 2004.
  16. Harary F: Graph theory. Adison Wesley. Massachusetts, 1972.
Index Terms

Computer Science
Information Sciences

Keywords

Complete bipartite Graph Factorization of Graph Symmetric Graph

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