ScholarLens Back to search
2012•Unpublished venueRequires access

On Total Domination Polynomial of Graphs

A. Vijayan, Sreedharan Sanal Kumar

Open publisher page 2 citations

Abstract

In this paper, we introduce the concept of total domination polynomial for any graph G. The total domination polynomial of a graph G of order n is the polynomial Dt(G, x) = Σ t(G, i) xi, where dt(G, i) is the number of total dominating sets of G of size i , and γt(G) is the total domination number of G. we obtain some properties of Dt(G, x) and its coefficients. Also, we calculate total domination polynomials for the complete graph Kn , the complete bipartite graph Km,n , GoK1 and Go􀜭m..

About this research paper

What this paper is about

In this paper, we introduce the concept of total domination polynomial for any graph G. The total domination polynomial of a graph G of order n is the polynomial Dt(G, x) = Σ t(G, i) xi, where dt(G, i) is the number of total dominating sets of G of size i , and γt(G) is the total domination number of G. we obtain some properties of Dt(G, x) and its coefficients. Also, we calculate total domination polynomials for the complete graph Kn , the complete bipartite graph Km,n , GoK1 and Go􀜭m..

Why it matters

OpenAlex reports 2 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

In this paper, we introduce the concept of total domination polynomial for any graph G. The total domination polynomial of a graph G of order n is the polynomial Dt(G, x) = Σ t(G, i) xi, where dt(G, i) is the number of total dominating sets of G of size i , and γt(G) is the total domination number of G. we obtain some properties of Dt(G, x) and its coefficients. Also, we calculate total domination polynomials for the complete graph Kn , the complete bipartite graph Km,n , GoK1 and Go􀜭m..

Key concepts: Combinatorics, Mathematics, Domination analysis, Bipartite graph, Graph, Dominating set, Discrete mathematics, Vertex (graph theory)

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
On Total Domination Polynomial of Graphs — Research Paper | ScholarLens