Research Article
A Computational Study for the Graph-theoretic Version of the Union-closed Sets Conjecture
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
|
| Volume 50 - Issue 12 |
| Published: July 2012 |
| Authors: M. I. Moussa, E. M. Badr |
10.5120/7820-0945
|
M. I. Moussa, E. M. Badr . A Computational Study for the Graph-theoretic Version of the Union-closed Sets Conjecture. International Journal of Computer Applications. 50, 12 (July 2012), 1-5. DOI=10.5120/7820-0945
@article{ 10.5120/7820-0945,
author = { M. I. Moussa,E. M. Badr },
title = { A Computational Study for the Graph-theoretic Version of the Union-closed Sets Conjecture },
journal = { International Journal of Computer Applications },
year = { 2012 },
volume = { 50 },
number = { 12 },
pages = { 1-5 },
doi = { 10.5120/7820-0945 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2012
%A M. I. Moussa
%A E. M. Badr
%T A Computational Study for the Graph-theoretic Version of the Union-closed Sets Conjecture%T
%J International Journal of Computer Applications
%V 50
%N 12
%P 1-5
%R 10.5120/7820-0945
%I Foundation of Computer Science (FCS), NY, USA
Abstract
An induced subgraph S of a graph G is called a derived subgraph of G if S contains no isolated vertices. An edge e of G is said to be residual if e occurs in more than half of the derived subgraphs of G. We prove some theorems which calculate the number of derived subgraphs for some special graphs. We also present a new algorithm SDSA that calculates the number of derived subgraphs for a given graph G and determines the residual and non-residual edges. Finally, we introduce a computational study which supports our results.
References
- I. Rival (Ed. ), Graphs And Order, Reidel, Dordrecht-Boston,(1985), p. 25.
- R. P. Stanley, Enumerative Combinatorics, vol. I, Wadsworth & Broks/Cole, Belmont, CA, (1986).
- B. Poonen, Union-Closed Families, J. Combin. Theory, A 59 (1992), 253-268.
- M. H. El-Zahar , A Graph-Theoretic Version Of The Union-Closed Sets Conjecture, J. Graph Theory 26 (1997), no. 3, 155-163.
- B. Llano, J. Montellano-Ballesteros, E. Rivera-Campo and R. Strauz " On Conjecture of Frankl and El-Zahar" J. Graph Theory 57: 344-352 (2008).
- G. Chartrand and L. Lesniak " Graphs & Digraphs" (third edition) Chaman & Hall, London, (1996) .
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