Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Monophonic domination polynomial of the path graph
View through CrossRef
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)
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.
Related Results
Domination of Polynomial with Application
Domination of Polynomial with Application
In this paper, .We .initiate the study of domination. polynomial , consider G=(V,E) be a simple, finite, and directed graph without. isolated. vertex .We present a study of the Ira...
Domination of polynomial with application
Domination of polynomial with application
In this paper, .We .initiate the study of domination. polynomial , consider G=(V,E) be a simple, finite, and directed graph without. isolated. vertex .We present a study of the Ira...
On the edge monophonic number of a graph
On the edge monophonic number of a graph
For a connected graph G = (V, E), an edge monophonic set of G is a set M?
V(G) such that every edge of G is contained in a monophonic path joining some
pair of vertices in M....
THE FORCING EDGE FIXING EDGE-TO-VERTEX MONOPHONIC NUMBER OF A GRAPH
THE FORCING EDGE FIXING EDGE-TO-VERTEX MONOPHONIC NUMBER OF A GRAPH
For a connected graph G = (V, E), a set Se ⊆ E(G)–{e} is called an edge fixing edge-to-vertex monophonic set of an edge e of a connected graph G if every vertex of G lies on an e –...
RESTRAINED DOUBLE MONOPHONIC NUMBER OF A GRAPH
RESTRAINED DOUBLE MONOPHONIC NUMBER OF A GRAPH
For a connected graph \(G\) of order at least two, a double monophonic set \(S\) of a graph \(G\) is a restrained double monophonic set if either \(S=V\) or the subgraph induced b...
On monophonic pebbling number
On monophonic pebbling number
Given a connected graph G and a configuration D of pebbles on V(G), a pebble move consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. A m...
Completion and decomposition of hypergraphs by domination hypergraphs
Completion and decomposition of hypergraphs by domination hypergraphs
A graph consists of a finite non-empty set of vertices and a set of unordered pairs of vertices, called edges. A dominating set of a graph is a set of vertices D such that every ve...
Monophonic Polynomial of the cartesian product of some graphs
Monophonic Polynomial of the cartesian product of some graphs
Let be the family of monophonic sets of a graph with cardinality and let Then the monophonic polynomial of is defined as , where is the monophonic number of . In this paper w...