منابع مشابه
Klazar trees and perfect matchings
Martin Klazar computed the total weight of ordered trees under 12 different notions of weight. The last and perhaps most interesting of these weights, w12, led to a recurrence relation and an identity for which he requested combinatorial explanations. Here we provide such explanations. To do so, we introduce the notion of a “Klazar violator” vertex in an increasing ordered tree and observe that...
متن کاملOn the kth Eigenvalues of Trees with Perfect Matchings
Let T + 2p be the set of all trees on 2p (p ≥ 1) vertices with perfect matchings. In this paper, we prove that for any tree T in T + 2p , the kth largest eigenvalue λk(T ) satisfies λk(T ) ≤ 1 2 “q ̊ p k ˇ − 1 + q ̊ p k ˇ + 3 ” (k = 1, 2, . . . , p). This upper bound is known to be best possible when k = 1. The set of trees obtained from a tree on p vertices by joining a pendent vertex to each ve...
متن کاملOrdering Trees with Perfect Matchings by Their Wiener Indices
The Wiener index of a connected graph is the sum of all pairwise distances of vertices of the graph. In this paper, we consider the Wiener indices of trees with perfect matchings, characterizing the eight trees with smallest Wiener indices among all trees of order 2 ( 11) m m with perfect matchings.
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 کاملPERFECT MATCHINGS AND k-DECOMPOSABILITY OF INCREASING TREES
A tree is called k-decomposable if it has a spanning forest whose components are all of size k. In this paper, we study the number of k-decomposable trees in families of increasing trees, i.e. labeled trees in which the unique path from the root to an arbitrary vertex forms an increasing sequence. Functional equations for the corresponding counting series are provided, yielding asymptotic or ev...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2003
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(02)00454-8