Independent sets of m, n-gonal graphs
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Publication Details
Author list: Khantavchai A., Jiarasuksakun T.
Publication year: 2016
Journal: Thai Journal of Mathematics (1686-0209)
Volume number: 14
Issue number: 1
Start page: 1
End page: 12
Number of pages: 12
ISSN: 1686-0209
Languages: English-Great Britain (EN-GB)
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Abstract
An m,n-gonal system π = (V,E,F), where V is a vertex set, E is an edge set and F is a face set, is a graph of cyclic hydrocarbon molecules: each vertex represents a carbon atom and each edge represents a chemical bond. A Kekule structure, K ⊆ E is a perfect matching and the edges of the matching correspond to double bonds. We count a number of perfect matchings (Kekule structures) in m,n-gonal systems where m, n ≡ 2(mod 4). Our result is shown that the number of perfect matchings is ϕ(π) = |detA(π)|, where A(π) is a biadjacency matrix for each system. Moreover, we study the interesting properties of vertex and face independence sets of m,n-gonal systems. © 2016 by the Mathematical Association of Thailand. All rights reserved.
Keywords
Cyclic hydro-carbon, Independent set, Kekule structure, m,n-gonal system
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