A remark on branch weights in countable trees

Bohdan Zelinka

The search session has expired. Please query the service again.

Displaying similar documents to “A remark on branch weights in countable trees”

Bounds On The Disjunctive Total Domination Number Of A Tree

Michael A. Henning, Viroshan Naicker (2016)

Discussiones Mathematicae Graph Theory

Similarity:

Let G be a graph with no isolated vertex. In this paper, we study a parameter that is a relaxation of arguably the most important domination parameter, namely the total domination number, γt(G). A set S of vertices in G is a disjunctive total dominating set of G if every vertex is adjacent to a vertex of S or has at least two vertices in S at distance 2 from it. The disjunctive total domination number, [...] γtd(G) $γ_{t}^{d} (G)$ , is the minimum cardinality of such a set. We observe that [...] γtd(G)≤γt(G)...

Arbitrarily vertex decomposable caterpillars with four or five leaves

Sylwia Cichacz, Agnieszka Görlich, Antoni Marczyk, Jakub Przybyło, Mariusz Woźniak (2006)

Discussiones Mathematicae Graph Theory

Similarity:

A graph G of order n is called arbitrarily vertex decomposable if for each sequence (a₁,...,aₖ) of positive integers such that a₁+...+aₖ = n there exists a partition (V₁,...,Vₖ) of the vertex set of G such that for each i ∈ 1,...,k, $V_{i}$ induces a connected subgraph of G on $a_{i}$ vertices. D. Barth and H. Fournier showed that if a tree T is arbitrarily vertex decomposable, then T has maximum degree at most 4. In this paper we give a complete characterization of arbitrarily vertex decomposable...

Closure for spanning trees and distant area

Jun Fujisawa, Akira Saito, Ingo Schiermeyer (2011)

Discussiones Mathematicae Graph Theory

Similarity:

A k-ended tree is a tree with at most k endvertices. Broersma and Tuinstra [3] have proved that for k ≥ 2 and for a pair of nonadjacent vertices u, v in a graph G of order n with $d e g_{G} u + d e g_{G} v \geq n - 1$ , G has a spanning k-ended tree if and only if G+uv has a spanning k-ended tree. The distant area for u and v is the subgraph induced by the set of vertices that are not adjacent with u or v. We investigate the relationship between the condition on $d e g_{G} u + d e g_{G} v$ and the structure of the distant area for u and v. We prove...

On locating and differentiating-total domination in trees

Mustapha Chellali (2008)

Discussiones Mathematicae Graph Theory

Similarity:

A total dominating set of a graph G = (V,E) with no isolated vertex is a set S ⊆ V such that every vertex is adjacent to a vertex in S. A total dominating set S of a graph G is a locating-total dominating set if for every pair of distinct vertices u and v in V-S, N(u)∩S ≠ N(v)∩S, and S is a differentiating-total dominating set if for every pair of distinct vertices u and v in V, N[u]∩S ≠ N[v] ∩S. Let $γ ₜ^{L} (G)$ and $γ ₜ^{D} (G)$ be the minimum cardinality of a locating-total dominating set and a differentiating-total...

Weak roman domination in graphs

P. Roushini Leely Pushpam, T.N.M. Malini Mai (2011)

Discussiones Mathematicae Graph Theory

Similarity:

Let G = (V,E) be a graph and f be a function f:V → 0,1,2. A vertex u with f(u) = 0 is said to be undefended with respect to f, if it is not adjacent to a vertex with positive weight. The function f is a weak Roman dominating function (WRDF) if each vertex u with f(u) = 0 is adjacent to a vertex v with f(v) > 0 such that the function f’: V → 0,1,2 defined by f’(u) = 1, f’(v) = f(v)-1 and f’(w) = f(w) if w ∈ V-u,v, has no undefended vertex. The weight of f is $w (f) = \sum_{v \in V} f (v)$ . The weak Roman domination...

Solution to the problem of Kubesa

Mariusz Meszka (2008)

Discussiones Mathematicae Graph Theory

Similarity:

An infinite family of T-factorizations of complete graphs $K_{2 n}$ , where 2n = 56k and k is a positive integer, in which the set of vertices of T can be split into two subsets of the same cardinality such that degree sums of vertices in both subsets are not equal, is presented. The existence of such T-factorizations provides a negative answer to the problem posed by Kubesa.

On the (2,2)-domination number of trees

You Lu, Xinmin Hou, Jun-Ming Xu (2010)

Discussiones Mathematicae Graph Theory

Similarity:

Let γ(G) and $γ_{2, 2} (G)$ denote the domination number and (2,2)-domination number of a graph G, respectively. In this paper, for any nontrivial tree T, we show that $(2 (γ (T) + 1)) / 3 \leq γ_{2, 2} (T) \leq 2 γ (T)$ . Moreover, we characterize all the trees achieving the equalities.

A note on the cubical dimension of new classes of binary trees

Kamal Kabyl, Abdelhafid Berrachedi, Éric Sopena (2015)

Czechoslovak Mathematical Journal

Similarity:

The cubical dimension of a graph $G$ is the smallest dimension of a hypercube into which $G$ is embeddable as a subgraph. The conjecture of Havel (1984) claims that the cubical dimension of every balanced binary tree with $2^{n}$ vertices, $n \geq 1$ , is $n$ . The 2-rooted complete binary tree of depth $n$ is obtained from two copies of the complete binary tree of depth $n$ by adding an edge linking their respective roots. In this paper, we determine the cubical dimension of trees obtained by subdividing twice...

On $k$ -pairable graphs from trees

Zhongyuan Che (2007)

Czechoslovak Mathematical Journal

Similarity:

The concept of the $k$ -pairable graphs was introduced by Zhibo Chen (On $k$ -pairable graphs, Discrete Mathematics 287 (2004), 11–15) as an extension of hypercubes and graphs with an antipodal isomorphism. In the same paper, Chen also introduced a new graph parameter $p (G)$ , called the pair length of a graph $G$ , as the maximum $k$ such that $G$ is $k$ -pairable and $p (G) = 0$ if $G$ is not $k$ -pairable for any positive integer $k$ . In this paper, we answer the two open questions raised by Chen in the case that the graphs...

On the spectral radius of $‡$ -shape trees

Xiaoling Ma, Fei Wen (2013)

Czechoslovak Mathematical Journal

Similarity:

Let $A (G)$ be the adjacency matrix of $G$ . The characteristic polynomial of the adjacency matrix $A$ is called the characteristic polynomial of the graph $G$ and is denoted by $φ (G, λ)$ or simply $φ (G)$ . The spectrum of $G$ consists of the roots (together with their multiplicities) $λ_{1} (G) \geq λ_{2} (G) \geq ... \geq λ_{n} (G)$ of the equation $φ (G, λ) = 0$ . The largest root $λ_{1} (G)$ is referred to as the spectral radius of $G$ . A $‡$ -shape is a tree with exactly two of its vertices having maximal degree 4. We will denote by $G (l_{1}, l_{2}, ..., l_{7})$ $(l_{1} \geq 0$ , $l_{i} \geq 1$ , $i = 2, 3, ..., 7)$ a $‡$ -shape tree such that...