Connected vertex–Edge dominating sets and connected vertex–Edge domination polynomials of triangular ladder

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Abstract

Let $G$ be a simple connected graph of order $n$. Let $D_{\text {cye }}(G, i)$ be the family of connected vertex-edge dominating sets of $G$ with cardinality $i$. The polynomial
Dcve (G,x)=i=γcve (G)ndcve (G,i)xi
is called the connected vertex - edge domination polynomial of $G$ where $d_{\text {cve }}(G, i)$ is the number of vertex edge dominating sets of $G$. In this paper, we study some properties of connected vertex - edge domination polynomials of the Triangular Ladder $T L_n$. We obtain a recursive formula for $d_{\text {cve }}\left(T L_{n, i}\right)$. Using this recursive formula, we construct the connected vertex - edge domination polynomial
Dcve (TLn,x)=i=n22ndcve(TLn,i)xi
of $T L_n$, where $D_{\text {cve }}\left(T L_{n, i}\right)$ is the number of connected vertex - edge dominating sets of $T L_n$ with cardinality $i$ and some properties of this polynomial have been studied.

Keywords:

Triangular ladder, Connected vertex – edge dominating set, connected vertex – edge domination number, connected vertex – edge domination polynomial

Mathematics Subject Classification:

Mathematics
  • V. S. Radhika Research Department of Mathematics, Nesamony Memorial Christian College [Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli-627012, Tamil Nadu, India.], Marthandam, Kanyakumari, Tamil Nadu, India.
  • A. Vijayan Research Department of Mathematics, Nesamony Memorial Christian College [Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli-627012, Tamil Nadu, India.], Marthandam, Kanyakumari, Tamil Nadu, India.
  • Pages: 474-479
  • Date Published: 01-01-2021
  • Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)

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Published

01-01-2021

How to Cite

V. S. Radhika, and A. Vijayan. “Connected vertex–Edge Dominating Sets and Connected vertex–Edge Domination Polynomials of Triangular Ladder”. Malaya Journal of Matematik, vol. 9, no. 01, Jan. 2021, pp. 474-9, https://www.malayajournal.org/index.php/mjm/article/view/1061.