Displaying similar documents to “Some new classes of graceful Lobsters obtained from diameter four trees”

A remark on branch weights in countable trees

Bohdan Zelinka (2004)

Mathematica Bohemica

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Let T be a tree, let u be its vertex. The branch weight b ( u ) of u is the maximum number of vertices of a branch of T at u . The set of vertices u of T in which b ( u ) attains its minimum is the branch weight centroid B ( T ) of T . For finite trees the present author proved that B ( T ) coincides with the median of T , therefore it consists of one vertex or of two adjacent vertices. In this paper we show that for infinite countable trees the situation is quite different.

Arbitrarily vertex decomposable caterpillars with four or five leaves

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

Discussiones Mathematicae Graph Theory

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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...

On k -pairable graphs from trees

Zhongyuan Che (2007)

Czechoslovak Mathematical Journal

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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...

Bounds On The Disjunctive Total Domination Number Of A Tree

Michael A. Henning, Viroshan Naicker (2016)

Discussiones Mathematicae Graph Theory

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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)...

Closure for spanning trees and distant area

Jun Fujisawa, Akira Saito, Ingo Schiermeyer (2011)

Discussiones Mathematicae Graph Theory

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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 ≥ 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...