The week's pick
Reseach 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 - Number 12 |
| Year of Publication: 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
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
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- 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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