Graphical properties of polyhexes: Perfect matching vector and forcing |
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Authors: | Frank Harary Douglas J Klein Tomislav P Živkovič |
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Institution: | (1) Department of Computer Science, New Mexico State University, 88003-0001 Las Cruces, NM, USA;(2) Department of Marine Sciences, Texas A&M University at Galveston, 77553-1675 Galveston, TX, USA;(3) Ruder Bo kovi Institute, Zagreb, 41001 Croatia, Yugoslavia |
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Abstract: | From the viewpoint of graph theory and its applications, subgraphs of the tiling of the plane with unit squares have long been studied in statistical mechanics, In organic chemistry, a much more relevant case concerns subgraphs of the tiling with unit hexagons. Our purpose here is to take a mathematical view of such polyhex graphsG and study two novel concepts concerning perfect matchingsM. First, the forcing number ofM is the smallest number of edges ofM which are not contained in any other perfect matching ofG. Second, the perfect matching vector ofM is written (n
3,n
2,n
1,n
0), wheren
k is the number of hexagons with exactlyk edges inM. We establish some initial results involving these two concepts and pose some questions. |
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Keywords: | |
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