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Dominating set

About: Dominating set is a research topic. Over the lifetime, 4058 publications have been published within this topic receiving 72432 citations. The topic is also known as: dominating set problem.


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27 Oct 2017
TL;DR: The critical and stability concept to strong fuzzy dominating set in fuzzy graphs is introduced and the node whose removal increases (or) decreases the strong fuzzy domination number is defined.
Abstract: I n this paper we introduce the critical and stability concept to strong fuzzy dominating set in fuzzy graphs. The strong fuzzy dominating critical node is a node whose removal increases (or) decreases the strong fuzzy domination number. The stability of strong fuzzy dominating set is the minimum number of nodes whose removal increases (or) decreases the strong domination number.
DOI
07 May 2021
TL;DR: In this paper, the concept of tree domination in middle and splitting graphs was introduced and the minimum cardinality of a dominating set of a graph G is defined as the domination number of G and is denoted by g(G).
Abstract: Let G = (V, E) be a connected graph. A subset D of V is called a dominating set of G if N[D] = V. The minimum cardinality of a dominating set of G is called the domination number of G and is denoted by g(G). A dominating set D of a graph G is called a tree dominating set (ntr - set) if the induced subgraph aDn is a tree. The tree domination number γtr(G) of G is the minimum cardinality of a tree dominating set. The Middle Graph M(G) of G is defined as follows. The vertex set of M(G) is V(G)EE(G). Two vertices x. y in the vertex set of M(G) are adjacent in M(G) if one of the following holds. (i) x, y are in E(G) and x, y are adjacent in G. (ii) xIV(G), yIE(G) and y is incident at x in G. Let G be a graph with vertex set V(G) and let V′(G) be a copy of V(G). The splitting graph S(G) of G is the graph, whose vertex set is V(G) E V′(G) and edge set is {uv, u′v and uv′: uvIE(G)}. In this paper we study the concept of tree domination in middle and splitting graphs.
Journal Article
TL;DR: The concept of externally fuzzy equitable dominating set is introduced and some interesting result is obtained for this new parameter in external equitable domination in fuzzy graphs.
Abstract: L et be a fuzzy graph. A subset of is called externally fuzzy equitable dominating set of if is a dominating set of and for every such that . for some . An externally fuzzy equitable dominating set is also called complementary fuzzy dominating set. The minimum cardinality of a minimal externally fuzzy equitable dominating set of is called externally fuzzy equitable domination number of and is denoted by . In this paper we introduce the concept of externally fuzzy equitable dominating set. Also we obtain some interesting result for this new parameter in external equitable domination in fuzzy graphs.
Journal ArticleDOI
TL;DR: This work provides characterizations of tcdd-critical graphs for the classes of block graphs, split graphs and unicyclic graphs and a characterization of cdd- critical cacti.
Abstract: A dominating set in a graph G=(V(G),E(G)) is a set D of vertices such that every vertex in V(G)\ D has a neighbor in D. A connected dominating set of a graph G is a dominating set whose induce subgraph is connected. The connected domination number gamma_c(G) is the minimum number of vertices of a connected dominating set of G. A graph G is connected domination dot-critical (cdd-critical) if contracting any two adjacent vertices decreases gamma_c(G); and G is totally connected domination dot-critical (tcdd-critical) if contracting any two vertices decreases gamma_c(G). We provide characterizations of tcdd-critical graphs for the classes of block graphs, split graphs and unicyclic graphs and a characterization of cdd-critical cacti.

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023142
2022265
2021248
2020248
2019268
2018239