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Monophonic domination polynomial of the path graph

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.

Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences)

P. Arul Paul Sudhahar W. Jebi

Notes on Number Theory and Discrete Mathematics

2024

Title: Monophonic domination polynomial of the path graph

Description:

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.

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Monophonic domination polynomial of the path graph

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