Domination polynomial of generalized book graphs

Saeid Alikhani, Somayeh Jahari


Let $G$ be a simple graph of order $n$.
The domination polynomial of $G$ is the polynomial
$D(G, x)=\sum_{i=0}^{n} d(G,i) x^{i}$,
where $d(G,i)$ is the number of dominating sets of $G$ of size $i$.
Let $n$ be any positive integer and  $B_n$ be the {\em $n$-book graphs}, formed by joining $n$ copies of the cycle graph $C_4$ with a common edge. In this paper, we  study the domination polynomials of some generalized book  graphs. In particular we examine the domination roots of these families, and find the limiting curve for the roots.

Full Text: PDF


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.