Monophonic domination polynomial of the path graph
Year: 2024
Type: article
Abstract: Let $MD(G, i)$ be the family of monophonic dominating sets of a graph $G$ with cardinality $i$ and let $\md(G, i) = |MD(G, i)|$. Then the monophonic domination polynomial $MD(G, x)$ of $G$ is defined as $MD(G, x) = \sum_{i = \gamma_m(G)}^{p} \md(G, i) x^i$, where $\gamma_m(G)$ is the monophonic domination number of $G$. In this paper we have determined the family of monophonic dominating sets of the path graph $P_n$ with cardinality $i$. Also, the monophonic domination polynomial of the path graph is calculated and some properties of the coefficient $\md(P_n, i)$ is discussed.
Authors: P. Arul Paul Sudhahar, W. Jebi
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404651410