A Computational Study for the Graph-theoretic Version of the Union-closed Sets Conjecture
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10.5120/7820-0945 |
M I Moussa and E M Badr. Article: A Computational Study for the Graph-theoretic Version of the Union-closed Sets Conjecture. International Journal of Computer Applications 50(12):1-5, July 2012. Full text available. BibTeX
@article{key:article,
author = {M. I. Moussa and E. M. Badr},
title = {Article: 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},
month = {July},
note = {Full text available}
}
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.
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