June 10, 2023
Doost Ali Mojdeh

Doost Ali Mojdeh

Degree: Professor
Address: Department of Mathematics, University of Mazandaran, Babolsar, Iran
Education: Ph.D in Mathematics (Graph Theory and Combinatorics)
Phone: 011-35302448
Faculty: Faculty of Mathematical Sciences


Title Connected domination polynomial of graphs
Type Article
connected domination polynomial, graphs, connected dominating set, Petersen graphs.
Journal Fasciculi Mathematici
DOI 10.1515/fascmath-2018-0007
Researchers Doost Ali Mojdeh (First researcher) , Azam Sadat Emadi (Second researcher)


Let $G$ be a simple graph of order $n$. The connected domination polynomial of $G$ is the polynomial $D_{c}(G, x)=\sum_{i=\gamma_{c}(G)}^{|V(G)|}d_{c}(G, i)x^i$, where $d_{c}(G, i)$ is the number of connected dominating sets of $G$ of size $i$ and $\gamma_{c}(G)$ is the connected domination number of $G$. In this paper we study $D_{c}(G, x)$ of any graph. We classify many families of graphs by studying their connected domination polynomial.