Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Domination index in graphs
View through CrossRef
The concepts of domination and topological index hold great significance within the realm of graph theory. Therefore, it is pertinent to merge these concepts to derive the domination index of a graph. A novel concept of the domination index is introduced, which utilizes the domination degree of a vertex. The domination degree of a vertex [Formula: see text] is defined as the minimum cardinality of a minimal dominating set (MDS) that includes [Formula: see text] Methods to find a MDS containing a particular vertex is also discussed in the study. The notion of domination degree and domination index are studied for graphs like complete graphs, complete bipartite, [Formula: see text] partite graphs, cycles, wheels, paths, book graphs, windmill graphs, Kragujevac trees. The study is extended to operation in graphs. Inequalities involving domination degree and already established graph parameters are discussed. An application of domination degree is discussed in facility allocation in a city.
World Scientific Pub Co Pte Ltd
Title: Domination index in graphs
Description:
The concepts of domination and topological index hold great significance within the realm of graph theory.
Therefore, it is pertinent to merge these concepts to derive the domination index of a graph.
A novel concept of the domination index is introduced, which utilizes the domination degree of a vertex.
The domination degree of a vertex [Formula: see text] is defined as the minimum cardinality of a minimal dominating set (MDS) that includes [Formula: see text] Methods to find a MDS containing a particular vertex is also discussed in the study.
The notion of domination degree and domination index are studied for graphs like complete graphs, complete bipartite, [Formula: see text] partite graphs, cycles, wheels, paths, book graphs, windmill graphs, Kragujevac trees.
The study is extended to operation in graphs.
Inequalities involving domination degree and already established graph parameters are discussed.
An application of domination degree is discussed in facility allocation in a city.
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...
Minimum Domination Energy of Some Derived Graphs
Minimum Domination Energy of Some Derived Graphs
In this study, we introduce and systematically explore the concept of minimum domination energy of derived graphs, representing a novel integration of two fundamental areas in grap...
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...
Weakly Modular Graphs and Nonpositive Curvature
Weakly Modular Graphs and Nonpositive Curvature
This article investigates structural, geometrical, and topological characterizations and properties of weakly modular graphs and of cell complexes derived from them. The unifying t...
Independent and total domination in antiprism graphs from convex polytopes
Independent and total domination in antiprism graphs from convex polytopes
Let [Formula: see text] be a connected graph. Antiprism graphs, defined as the skeletons of antiprism-shaped convex polytopes, consist of [Formula: see text] vertices and [Formula:...
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...
Linear programming formulation for some generalized domination parameters
Linear programming formulation for some generalized domination parameters
An enormous number of domination parameters have been defined and studied, because of their applications in various fields of science and engineering. From it, we have selected som...
Independent Set in Neutrosophic Graphs
Independent Set in Neutrosophic Graphs
New setting is introduced to study neutrosophic independent number and independent neutrosophic-number arising neighborhood of different vertices. Neighbor is a key term to have th...