Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Some new results on captive dominating sets in graphs
View through CrossRef
A dominating set [Formula: see text] is said to be a captive dominating set of [Formula: see text] if [Formula: see text] has no isolated vertex ([Formula: see text] is a total dominating set) and each vertex [Formula: see text] is adjacent to at least one vertex in [Formula: see text]. A captive dominating set [Formula: see text] is said to be a minimal captive dominating set if no proper subset [Formula: see text] of [Formula: see text] is a captive dominating set. The minimum cardinality of a minimal captive dominating set of [Formula: see text] is called the captive domination number of [Formula: see text] which is denoted by [Formula: see text]. In this paper, we have characterized some results, determine the values of the domination-related parameters for the graph and its splitting graph, relate captive domination and packing number of a graph, etc. We have also constructed graphs for which [Formula: see text]
World Scientific Pub Co Pte Ltd
Title: Some new results on captive dominating sets in graphs
Description:
A dominating set [Formula: see text] is said to be a captive dominating set of [Formula: see text] if [Formula: see text] has no isolated vertex ([Formula: see text] is a total dominating set) and each vertex [Formula: see text] is adjacent to at least one vertex in [Formula: see text].
A captive dominating set [Formula: see text] is said to be a minimal captive dominating set if no proper subset [Formula: see text] of [Formula: see text] is a captive dominating set.
The minimum cardinality of a minimal captive dominating set of [Formula: see text] is called the captive domination number of [Formula: see text] which is denoted by [Formula: see text].
In this paper, we have characterized some results, determine the values of the domination-related parameters for the graph and its splitting graph, relate captive domination and packing number of a graph, etc.
We have also constructed graphs for which [Formula: see text].
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...
New results on connected dominating structures in graphs
New results on connected dominating structures in graphs
Abstract
A set of vertices in a graph is a dominating set if every vertex not in the set is adjacent to at least one vertex in the set. A dominating structure is a s...
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...
Predictable and host-species specific humanization of the gut microbiota in captive primates
Predictable and host-species specific humanization of the gut microbiota in captive primates
Humans and non-human primates (NHPs) harbor complex gut microbial
communities that affect phenotypes and fitness. The gut microbiotas of
wild NHPs reflect their hosts’ phylogenetic...
The Minimum Superior Dominating Energy of Graphs
The Minimum Superior Dominating Energy of Graphs
Kathiresan and Marimuthu were the pioneers of superior distance in graphs. The same authors put forth the concept of superior domination in 2008. Superior distance is the shortest ...
Computing the Energy of Certain Graphs based on Vertex Status
Computing the Energy of Certain Graphs based on Vertex Status
Background:
The concept of Hückel molecular orbital theory is used to compute the graph energy numerically and graphically on the base of the status of a vertex.
Objective:
Our a...
Data Analytics on Graphs Part I: Graphs and Spectra on Graphs
Data Analytics on Graphs Part I: Graphs and Spectra on Graphs
The area of Data Analytics on graphs promises a paradigm shift, as we approach information processing of new classes of data which are typically acquired on irregular but structure...
Twilight graphs
Twilight graphs
AbstractThis paper deals primarily with countable, simple, connected graphs and the following two conditions which are trivially satisfied if the graphs are finite:(a) there is an ...