منابع مشابه
Fibonacci Numbers and the Numbers of Perfect Matchings of Square, Pentagonal, and Hexagonal Chains*
Let G be a finite graph. A perfect matching in G is a selection of edges in G such that each vertex of G belongs to exactly one selected edge. Therefore, if the number of vertices in G is odd, then there is no perfect matching. We denote by K(G) the number of perfect matchings of £, and refer to it as the K number of G. By a polygonal chain Py, s we mean a finite graph obtained by concatenating...
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The Wiener index is the sum of distances between all pairs of vertices in a connected graph. In this paper, explicit expressions for the expected value of the Wiener index of three types of random pentagonal chains (cf. Figure 1) are obtained.
متن کاملThe number of maximal matchings in polyphenylene chains
A matching is maximal if no other matching contains it as a proper subset. Maximal matchings model phenomena across many disciplines, including applications within chemistry. In this paper, we study maximal matchings in an important class of chemical compounds: polyphenylenes. In particular, we determine the extremal polyphenylene chains in regards to the number of maximal matchings. We also de...
متن کاملwiener numbers of random pentagonal chains
the wiener index is the sum of distances between all pairs of vertices in a connected graph. in this paper, explicit expressions for the expected value of the wiener index of three types of random pentagonal chains (cf. figure 1) are obtained.
متن کاملMarkov chains for sampling matchings
Markov Chain Monte Carlo algorithms are often used to sample combinatorial structures such as matchings and independent sets in graphs. A Markov chain is defined whose state space includes the desired sample space, and which has an appropriate stationary distribution. By simulating the chain for a sufficiently large number of steps, we can sample from a distribution arbitrarily close to the sta...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1984
ISSN: 0166-218X
DOI: 10.1016/0166-218x(84)90076-3