Pendant Total Domination Polynomial of Some Families of Standard Graphs

Jyoti Rani; Seema Mehra

doi:10.26713/cma.v14i2.2193

Authors

Jyoti Rani Department of Mathematics, Maharshi Dayanand University, Rohtak 124001, Haryana, India https://orcid.org/0000-0002-3233-2910 (unauthenticated)
Seema Mehra Department of Mathematics, Maharshi Dayanand University, Rohtak 124001, Haryana, India https://orcid.org/0000-0001-7219-9387 (unauthenticated)

DOI:

https://doi.org/10.26713/cma.v14i2.2193

Keywords:

Dominating Set (DS), Total Dominating Set (TDS), Pendant Total Domination (PTD), Pendant Total Dominating Set (PTDS), Pendant Total Domination Number (PTDN)

Abstract

In this article, our aim is to determine the pendant total domination polynomial of some families of standard graphs and obtain some properties of coefficients and nullity of the pendant total domination polynomial of a connected graph \(\mathcal{G}\). Consider \(\mathcal{G}\) as a simple connected graph and its vertex and edge sets are defined as \(\mathcal{V}_\calG\) and \(\mathcal{E}_\calG\), respectively. A set \(\mathcal{T} \subseteq \mathcal{V}_\calG\) is said to be a total dominating set of graph \(\mathcal{G}\) if all the vertices of the graph must attached with some vertex of \(\mathcal{T} \). A set \(\mathcal{T} \subseteq \mathcal{V}_\calG\) is said to be a PTDS if \(\mathcal{T}\) is a TDS and \(\langle \mathcal{T} \rangle\) contains at least a single pendant vertex.

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