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Computer generation of king and color polynomials of graphs and lattices and their applications to statistical mechanics

✍ Scribed by K. Balasubramanian; R. Ramaraj

Publisher: John Wiley and Sons
Year: 1985
Tongue: English
Weight: 631 KB
Volume: 6
Category: Article
ISSN: 0192-8651
DOI: 10.1002/jcc.540060513

No coin nor oath required. For personal study only.

✦ Synopsis

A computer program is developed in Pascal for the generation of king and color polynomials of graphs. The king polynomial was defined by Motoyama and Hosoya and was shown to be useful in dimer statistics, enumera.tion of Kekule structures, etc. We show that the king polynomial of a lattice is the same as the color polynomial of the associated dualist graph, where the color polynomial is defined here as the number of ways of coloring the vertices of a graph with one type of color (say, green) such that two adjacent vertices are not colored with the same color method of lattice statistics are outlined.

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