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2010•AKCE International Journal of Graphs and CombinatoricsRequires access

On total domination and support vertices of a tree

Ermelinda DeLaViña, C. E. Larson, Ryan Pepper, Bill Waller, Odile Favaron

Open publisher page 5 citations

Abstract

The total domination number γt(G) of a simple, undirected graph G is the order of a smallest subset D of the vertices of G such that each vertex of G is adjacent to some vertex in D. In this paper we prove two new upper bounds on the total domination number of a tree related to particular support vertices (vertices adjacent to leaves) of the tree. One of these bounds improves a 2004 result of Chellali and Haynes [1]. In addition, we prove some bounds on the total domination ratio of trees.

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What this paper is about

The total domination number γt(G) of a simple, undirected graph G is the order of a smallest subset D of the vertices of G such that each vertex of G is adjacent to some vertex in D. In this paper we prove two new upper bounds on the total domination number of a tree related to particular support vertices (vertices adjacent to leaves) of the tree. One of these bounds improves a 2004 result of Chellali and Haynes [1]. In addition, we prove some bounds on the total domination ratio of trees.

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OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The total domination number γt(G) of a simple, undirected graph G is the order of a smallest subset D of the vertices of G such that each vertex of G is adjacent to some vertex in D. In this paper we prove two new upper bounds on the total domination number of a tree related to particular support vertices (vertices adjacent to leaves) of the tree. One of these bounds improves a 2004 result of Chellali and Haynes [1]. In addition, we prove some bounds on the total domination ratio of trees.

Key concepts: Combinatorics, Mathematics, Vertex (graph theory), Undirected graph, Domination analysis, Graph, Neighbourhood (mathematics), Upper and lower bounds

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