منابع مشابه
Matchings in starlike trees
1. I N T R O D U C T I O N Ordering of graphs with respect to the number of matchings, and finding the graphs extremal with regard to this property, has been the topic of several earlier works [1-4]. These results have chemical applications, in connection with the so-called total 1r-electron energy [5-7]. Let G be a graph without loops and multiple edges. For k being a positive integer, m ( G ,...
متن کاملGraphs cospectral with starlike trees
A tree which has exactly one vertex of degree greater than two is said to be starlike. In spite of seemingly simple structure of these trees, not much is known about their spectral properties. In this paper, we introduce a generalization of the notion of cospectrality called m-cospectrality which turns out to be useful in constructing cospectral graphs. Based on this, we construct cospectral ma...
متن کاملStable Matchings in Trees
The maximum stable matching problem (Max-SMP) and the minimum stable matching problem (Min-SMP) have been known to be NP-hard for subcubic bipartite graphs, while Max-SMP can be solved in polynomal time for a bipartite graph G with a bipartition (X,Y ) such that degG(v) ≤ 2 for any v ∈ X. This paper shows that both Max-SMP and Min-SMP can be solved in linear time for trees. This is the first po...
متن کاملTrees and Matchings
In this article, Temperley’s bijection between spanning trees of a subgraph of the square grid on the one hand, and perfect matchings (also known as dimer coverings) of an associated subgraph of the square grid on the other, is extended to the setting of general planar directed (and undirected) graphs, where edges carry nonnegative weights that induce a weighting on the set of spanning trees. W...
متن کاملMatchings and phylogenetic trees.
This paper presents a natural coordinate system for phylogenetic trees using a correspondence with the set of perfect matchings in the complete graph. This correspondence produces a distance between phylogenetic trees, and a way of enumerating all trees in a minimal step order. It is useful in randomized algorithms because it enables moves on the space of trees that make random optimization str...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2001
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(01)00054-4