Counting Matching Numbers in Catacondensed Polyomino Systems

The matching counting problem has its own significance in mathematics and interconnection network of parallel computer system. Let G be a graph, the total matching number is the total number of independent edge subsets in G . For general graphs, the matching counting problem has proven to be intractable and computing the total matching number is #P hard. This has led to an emphasis on studying this problem in particular classes of graphs. The polyomino system is a finite 2connected plane graph such that each interior face (or say a cell) is surrounded by a regular square of length one. The catacondensed polyomino system is a chain polyomino system and its central line forms a tree. In this paper, the reduction formulas of computing the total matching number of any catacondensed polyomino system via three kinds of transfer matrices are obtained.