On the rules for the elimination of the non-canonical Morgan trees
Damir Vukičević (2009)
Kragujevac Journal of Mathematics
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Damir Vukičević (2009)
Kragujevac Journal of Mathematics
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Zoran Stanić (2006)
Publications de l'Institut Mathématique
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Bohdan Zelinka (1991)
Mathematica Bohemica
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Two types of a distance between isomorphism classes of graphs are adapted for rooted trees.
Lang, Wolfdieter (2009)
Journal of Integer Sequences [electronic only]
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Brouwer, A.E. (2008)
The Electronic Journal of Combinatorics [electronic only]
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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.
Callan, David (2003)
Journal of Integer Sequences [electronic only]
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Alameddine, A.F. (1991)
International Journal of Mathematics and Mathematical Sciences
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Katarzyna Jesse-Józefczyk (2012)
Open Mathematics
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Let G = (V, E) be a graph. A global secure set SD ⊆ V is a dominating set which satisfies the condition: for all X ⊆ SD, |N[X] ∩ SD| ≥ | N[X] − SD|. A global defensive alliance is a set of vertices A that is dominating and satisfies a weakened condition: for all x ∈ A, |N[x] ∩ A| ≥ |N[x] − A|. We give an upper bound on the cardinality of minimum global secure sets in cactus trees. We also present some results for trees, and we relate them to the known bounds on the minimum cardinality...
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...
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,...