| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 419398 | Discrete Applied Mathematics | 2013 | 8 Pages |
Abstract
Let G=(V,E)G=(V,E) be a connected graph, where |E||E| is even. In this paper we show that the line graph L(G)L(G) of GG contains at least 2|E|−|V|+12|E|−|V|+1 perfect matchings, and characterize GG such that L(G)L(G) has exactly 2|E|−|V|+12|E|−|V|+1 perfect matchings. As applications, we use a unified approach to solve the dimer problem on the Kagomé lattice, 3.12.123.12.12 lattice, and Sierpinski gasket with dimension two in the context of statistical physics.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Fengming Dong, Weigen Yan, Fuji Zhang,