Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Monophonic Polynomial of the cartesian product of some graphs
View through CrossRef
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 we have determined the sufficient condition for the monophonic set of . Also, we have calculated the monophonic polynomial of the cartesian product of some specific graphs by generating function method.
Science Research Society
Title: Monophonic Polynomial of the cartesian product of some graphs
Description:
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 we have determined the sufficient condition for the monophonic set of .
Also, we have calculated the monophonic polynomial of the cartesian product of some specific graphs by generating function method.
Related Results
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....
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...
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 –...
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...
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...
Monophonic domination polynomial of the path graph
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)...
Computing a Minimum Subset Feedback Vertex Set on Chordal Graphs Parameterized by Leafage
Computing a Minimum Subset Feedback Vertex Set on Chordal Graphs Parameterized by Leafage
Abstract
Chordal graphs are characterized as the intersection graphs of subtrees in a tree and such a representation is known as the tree model. Restricting the characteriz...
A New Alternative to Szeged, Mostar, and PI Polynomials—The SMP Polynomials
A New Alternative to Szeged, Mostar, and PI Polynomials—The SMP Polynomials
Szeged-like topological indices are well-studied distance-based molecular descriptors, which include, for example, the (edge-)Szeged index, the (edge-)Mostar index, and the (vertex...