On minimal energies of trees with given diameter.
Li, Shuchao, Li, Nana (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Li, Shuchao, Li, Nana (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Damian Bogdanowicz, Krzysztof Giaro (2013)
International Journal of Applied Mathematics and Computer Science
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The Robinson-Foulds (RF) distance is the most popular method of evaluating the dissimilarity between phylogenetic trees. In this paper, we define and explore in detail properties of the Matching Cluster (MC) distance, which can be regarded as a refinement of the RF metric for rooted trees. Similarly to RF, MC operates on clusters of compared trees, but the distance evaluation is more complex. Using the graph theoretic approach based on a minimum-weight perfect matching in bipartite graphs,...
Zoran Stanić (2006)
Publications de l'Institut Mathématique
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Masayoshi Matsushita, Yota Otachi, Toru Araki (2015)
Discussiones Mathematicae Graph Theory
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Two spanning trees T1 and T2 of a graph G are completely independent if, for any two vertices u and v, the paths from u to v in T1 and T2 are internally disjoint. For a graph G, we denote the maximum number of pairwise completely independent spanning trees by cist(G). In this paper, we consider cist(G) when G is a partial k-tree. First we show that [k/2] ≤ cist(G) ≤ k − 1 for any k-tree G. Then we show that for any p ∈ {[k/2], . . . , k − 1}, there exist infinitely many k-trees G such...
Damir Vukičević (2009)
Kragujevac Journal of Mathematics
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Damian Bogdanowicz (2011)
Applicationes Mathematicae
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The reconstruction of evolutionary trees is one of the primary objectives in phylogenetics. Such a tree represents historical evolutionary relationships between different species or organisms. Tree comparisons are used for multiple purposes, from unveiling the history of species to deciphering evolutionary associations among organisms and geographical areas. In this paper, we describe a general method for comparing phylogenetic trees and give some basic properties of the Matching Split...
Mustapha Chellali, Lutz Volkmann (2011)
Discussiones Mathematicae Graph Theory
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Let G = (V(G),E(G)) be a simple graph, and let k be a positive integer. A subset D of V(G) is a k-dominating set if every vertex of V(G) - D is dominated at least k times by D. The k-domination number γₖ(G) is the minimum cardinality of a k-dominating set of G. In [5] Volkmann showed that for every nontrivial tree T, γ₂(T) ≥ γ₁(T)+1 and characterized extremal trees attaining this bound. In this paper we characterize all trees T with γ₂(T) = γ₁(T)+2.
Đuro Kurepa (1968)
Publications de l'Institut Mathématique
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Brouwer, A.E. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Z. A. Łomnicki (1973)
Applicationes Mathematicae
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Callan, David (2003)
Journal of Integer Sequences [electronic only]
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Chen, William Y.C., Yan, Sherry H.F. (2006)
The Electronic Journal of Combinatorics [electronic only]
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D. Kurepa (1977)
Publications de l'Institut Mathématique [Elektronische Ressource]
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