Independent Sets of m,n-gonal Graphs

Asekha Khantavchai, Thiradet Jiarasuksakun

Abstract


An m,n-gonal system pi=(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\subseteq E  is a perfect matching and the edges of  the matching correspondto double bonds. We count a number of perfect matchings (Kekule structures) in m,n-gonal systems where  m,n = 2(mod4). Ourresult is shown that the number of perfect matchings is phi(pi)=|detA(pi)|, where A(pi) is a biadjacency matrix for each system.

Moreover, we study the interesting properties of  vertex and face independence sets of m,n-gonal systems.


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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|