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Path Factorization Induced Network Flow

by U S Rajput, Bal Govind Shukla
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 121 - Number 16
Year of Publication: 2015
Authors: U S Rajput, Bal Govind Shukla
10.5120/21626-4929

U S Rajput, Bal Govind Shukla . Path Factorization Induced Network Flow. International Journal of Computer Applications. 121, 16 ( July 2015), 30-39. DOI=10.5120/21626-4929

@article{ 10.5120/21626-4929,
author = { U S Rajput, Bal Govind Shukla },
title = { Path Factorization Induced Network Flow },
journal = { International Journal of Computer Applications },
issue_date = { July 2015 },
volume = { 121 },
number = { 16 },
month = { July },
year = { 2015 },
issn = { 0975-8887 },
pages = { 30-39 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume121/number16/21626-4929/ },
doi = { 10.5120/21626-4929 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T23:09:23.057747+05:30
%A U S Rajput
%A Bal Govind Shukla
%T Path Factorization Induced Network Flow
%J International Journal of Computer Applications
%@ 0975-8887
%V 121
%N 16
%P 30-39
%D 2015
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In path factorization Ushio [8] gave the necessary and sufficient conditions for P_k design. When k is an even number, the spectrum problem is completely solved [9, 1]. For odd value of k the problem was studied by several researchers [7, 10, 11, 5, 2, 6]. In all these papers [7, 10, 11, 5, 2, 6] Ushio Conjecture [8] played an important role. Here in this paper we obtain a feasible network flow consisting of path factors of a bipartite graph satisfying the conditions of path factorization.

References
  1. Beliang Du: P_2k-factorization of complete bipartite multigraph. Australasian Journal of Combinatorics 21(2000), 197 - 199.
  2. Du B and Wang J: P_(4k-1)-factorization of complete bipartite graphs. Science in China Ser. A Mathematics 48 (2005) 539 – 547.
  3. Ford L R, Fulkerson D R. "Maximum Flow through a Network". Canadian journal of Mathematics 8:399(1956).
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  5. Rajput U S and Shukla Bal Govind: P_9-factorization of complete bipartite graphs. Applied Mathematical Sciences, volume 5(2011), 921- 928.
  6. Rajput U S and Shukla Bal Govind: P_(4k+1)-factorization of complete bipartite graphs: Elixir Dis. Math. 45 (2012) 7893-7897.
  7. Ushio K: P_3-factorization of complete bipartite graphs. Discrete math. 72 (1988) 361-366.
  8. Ushio K: G-designs and related designs, Discrete Math. , 116(1993), 299-311.
  9. Wang H: P_2p-factorization of a complete bipartite graph, discrete math. 120 (1993) 307-308.
  10. Wang J and Du B: P_5-factorization of complete bipartite graphs. Discrete math. 308 (2008) 1665 – 1673.
  11. Wang J : P_7-factorization of complete bipartite graphs. Australasian Journal of Combinatorics, volume 33 (2005), 129-137.
Index Terms

Computer Science
Information Sciences

Keywords

Complete bipartite Graph Factorization of Graph Network Flow.

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