Global Forcing Number of Benzenoid Graphs |
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Authors: | Tomislav Do?li? |
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Institution: | (1) Department of Informatics and Mathematics, Faculty of Agriculture, University of Zagreb, Svetošimunska c. 25, 10000 Zagreb, Croatia |
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Abstract: | A global forcing set in a simple connected graph G with a perfect matching is any subset S of E(G) such that the restriction of the characteristic function of perfect matchings of G on S is an injection. The number of edges in a global forcing set of the smallest cardinality is called the global forcing number
of G. In this paper we prove several results concerning global forcing sets and numbers of benzenoid graphs. In particular, we
prove that all catacondensed benzenoids and catafused coronoids with n hexagons have the global forcing number equal to n, and that for pericondensed benzenoids the global forcing number is always strictly smaller than the number of hexagons. |
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Keywords: | global forcing number benzenoid graph |
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