N ov 2 00 5 Enumeration of perfect matchings of a type of Cartesian products of graphs ∗
نویسنده
چکیده
Let G be a graph and let Pm(G) denote the number of perfect matchings of G. We denote the path with m vertices by Pm and the Cartesian product of graphs G and H by G×H. In this paper, as the continuance of our paper [19], we enumerate perfect matchings in a type of Cartesian products of graphs by the Pfaffian method, which was discovered by Kasteleyn. Here are some of our results: 1. Let T be a tree and let Cn denote the cycle with n vertices. Then Pm(C4 ×T ) =
منابع مشابه
Enumeration of perfect matchings of a type of Cartesian products of graphs
Let G be a graph and let Pm(G) denote the number of perfect matchings of G. We denote the path with m vertices by Pm and the Cartesian product of graphs G and H byG×H . In this paper, as the continuance of our paper [W.Yan, F. Zhang, Enumeration of perfect matchings of graphs with reflective symmetry by Pfaffians, Adv. Appl. Math. 32 (2004) 175–188], we enumerate perfect matchings in a type of ...
متن کاملPfaffian Orientation and Enumeration of Perfect Matchings for some Cartesian Products of Graphs
The importance of Pfaffian orientations stems from the fact that if a graph G is Pfaffian, then the number of perfect matchings of G (as well as other related problems) can be computed in polynomial time. Although there are many equivalent conditions for the existence of a Pfaffian orientation of a graph, this property is not well-characterized. The problem is that no polynomial algorithm is kn...
متن کاملPerfect Matchings in Edge-Transitive Graphs
We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...
متن کاملSecret Sharing Based On Cartesian product Of Graphs
The purpose of this paper is to study the information ratio of perfect secret sharing of product of some special families of graphs. We seek to prove that the information ratio of prism graphs $Y_{n}$ are equal to $frac{7}{4}$ for any $ngeq 5$, and we will gave a partial answer to a question of Csirmaz cite{CL}. We will also study the information ratio of two other families $C_{m}times C_{n}$ a...
متن کاملPerfect Matchings of Cellular Graphs
We introduce a family of graphs, called cellular, and consider the problem of enumerating their perfect matchings. We prove that the number of perfect matchings of a cellular graph equals a power of 2 tiroes the number of perfect matchings of a certain subgraph, called the core of the graph. This yields, as a special case, a new proof of the fact that the Aztec diamond graph of order n introduc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011