Relatively prime dominating polynomial in graphs
Authors :
C. Jayasekaran 1 * and A. Jancy Vini 2
Author Address :
1 Department of Mathematics, **Pioneer Kumaraswamy College, Nagercoil-629003, Tamil Nadu, India
2 Department of Mathematics, **Holy Cross College (Autonomous), Nagercoil-629004, Tamil Nadu, India
*Corresponding author.
Abstract :
We introduce the concept of relatively prime domination polynomial of a graph $G$. The relatively prime domination polynomial of a graph $G$ of order $n$ is the polynomial $D_{rpd} (G,x)=\sum _{k=\gamma_{rpd}(G)}^{n} d_{rpd} (G,k) x^k$ where $d_{rpd}(G, k)$ is the number of relatively prime dominating sets of $G$ of size $k$, and $\gamma_{rpd}(G)$ is the relatively prime domination number of $G$. We compute this polynomial for path $P_n$, complete bipartite graph $K_{m, n}$, star $K_{1, n}$, bistar $B_{m, n}$, spider graph $K_{1, n, n}$ and Helm graph $H_n$.
Keywords :
Dominating polynomial, relatively prime dominating polynomial, relatively prime dominating polynomial roots.
DOI :
Article Info :
Received : July 01, 2019; Accepted : September 09, 2019.
