ScholarLens Back to search
1995•Journal of Beijing Institute of TechnologyRequires access

An Upper Bound for Total Domination Number

Liang Sun

Open publisher page 7 citations

Abstract

Let G=(V, E) be a simple graph without an isolate. A subset T of V is a total dominating set of G if for any there exists at least one vertex such that .The total domination number γ1(G) of G is the minimum order of a total dominating set of G. This paper proves that if G is a connected graph with n≥3 vertices and minimum degree at least two.

About this research paper

What this paper is about

Let G=(V, E) be a simple graph without an isolate. A subset T of V is a total dominating set of G if for any there exists at least one vertex such that .The total domination number γ1(G) of G is the minimum order of a total dominating set of G. This paper proves that if G is a connected graph with n≥3 vertices and minimum degree at least two.

Why it matters

OpenAlex reports 7 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Let G=(V, E) be a simple graph without an isolate. A subset T of V is a total dominating set of G if for any there exists at least one vertex such that .The total domination number γ1(G) of G is the minimum order of a total dominating set of G. This paper proves that if G is a connected graph with n≥3 vertices and minimum degree at least two.

Key concepts: Domination analysis, Dominating set, Combinatorics, Mathematics, Vertex (graph theory), Graph, Simple graph, Bound graph

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
An Upper Bound for Total Domination Number — Research Paper | ScholarLens