A note on reconstructing of finite trees from small subtrees
Václav Nýdl (1990)
Acta Universitatis Carolinae. Mathematica et Physica
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Václav Nýdl (1990)
Acta Universitatis Carolinae. Mathematica et Physica
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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.
Lamathe, Cédric (2004)
Journal of Integer Sequences [electronic only]
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Damir Vukičević (2009)
Kragujevac Journal of Mathematics
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Cameron, Peter J. (1995)
The Electronic Journal of Combinatorics [electronic only]
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Bostjan Brešar, Wilfried Imrich, Sandi Klavžar (2003)
Discussiones Mathematicae Graph Theory
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Tree-like isometric subgraphs of hypercubes, or tree-like partial cubes as we shall call them, are a generalization of median graphs. Just as median graphs they capture numerous properties of trees, but may contain larger classes of graphs that may be easier to recognize than the class of median graphs. We investigate the structure of tree-like partial cubes, characterize them, and provide examples of similarities with trees and median graphs. For instance, we show that the cube graph...
Brouwer, A.E. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Xiaoling Zhang, Kecai Deng (2017)
Discussiones Mathematicae Graph Theory
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An L(2, 1, 1)-labeling of a graph G is an assignment of non-negative integers (labels) to the vertices of G such that adjacent vertices receive labels with difference at least 2, and vertices at distance 2 or 3 receive distinct labels. The span of such a labelling is the difference between the maximum and minimum labels used, and the minimum span over all L(2, 1, 1)-labelings of G is called the L(2, 1, 1)-labeling number of G, denoted by λ2,1,1(G). It was shown by King, Ras and Zhou...
Alameddine, A.F. (1991)
International Journal of Mathematics and Mathematical Sciences
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You Lu, Xinmin Hou, Jun-Ming Xu, Ning Li (2010)
Discussiones Mathematicae Graph Theory
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Let γₜ(G) and γ₂(G) be the total domination number and the 2-domination number of a graph G, respectively. It has been shown that: γₜ(T) ≤ γ₂(T) for any tree T. In this paper, we provide a constructive characterization of those trees with equal total domination number and 2-domination number.
E. Kowalska (1987)
Applicationes Mathematicae
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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.