We apologize for a recent technical issue with our email system, which temporarily affected account activations. Accounts have now been activated. Authors may proceed with paper submissions. PhDFocusTM
CFP last date
20 December 2024
Call for Paper
January Edition
IJCA solicits high quality original research papers for the upcoming January edition of the journal. The last date of research paper submission is 20 December 2024

Submit your paper
Know more
The week's pick
Responsive image
Improved Shuffled Frog Leaping Algorithm with Self-Adaptive Shuffling for Fuzzy Logic PD+G Controller Optimization in Robotic Manipulators

Duc Hoang Nguyen
Random Articles
Reseach Article

P h_(4k-1)-Factorization of Symmetric Complete Bipartite Digraph

by U S Rajput, Bal Govind Shukla
journal cover thumbnail

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

Powered by PhDFocusTM