Results 1 to 10 of about 4,392 (255)

Medium Domination Decomposition of Graphs

Ratio Mathematica, 2022
A set of vertices  in a graph  dominates  if every vertex in  is either in  or adjacent to a vertex in . The size of any smallest dominating set is called domination number of .
E Ebin Raja Merly, Saranya J
doaj   +1 more source

New bound on MIS and MIN-CDS for a unit ball graph

ICT Express, 2017
The size of the maximum independent set (MIS) in a graph G is called the independence number. The size of the minimum connected dominating set (MIN-CDS) in G is called the connected domination number.
D.A. Mojdeh, M. Ghanbari, M. Ramezani
doaj   +1 more source

Valency based domination number for Mycielskian of some graphs‎ [PDF]

Mathematics and Computational Sciences
Let G = (V, E) be a connected graph and γvb(G) denotes the valency based domination number of G or simply vb-domination number of G. In this paper, analogous to isolated vertex in domination, defined valency based isolated vertex (or simply, vb-isolated ...
Kavitha Thilakan, Karakkattu Subrahmanian Parvathy   +1 more
doaj   +1 more source

Triameter of Graphs

Discussiones Mathematicae Graph Theory, 2021
In this paper, we study a new distance parameter triameter of a connected graph G, which is defined as max{d(u; v)+d(v;w)+d(u;w) : u; v;w ∈ V }and is denoted by tr(G).
Das Angsuman
doaj   +1 more source

Split Domination Number in Edge Semi-Middle Graph

Pan-American Journal of Mathematics, 2022
Let G = (p, q) be a connected graph and Me(G) be its corresponding edge semi-middle graph. A dominating set D ⊆ V [Me(G)] is split dominating set V [Me(G)] – D is disconnected.
Venkanagouda M. Goudar, K.C. Rajendra Prasad, K.M. Niranjan   +2 more
doaj   +1 more source

Weakly connected domination critical graphs [PDF]

Opuscula Mathematica, 2008
A dominating set \(D \subset V(G)\) is a weakly connected dominating set in \(G\) if the subgraph \(G[D]_w = (N_{G}[D],E_w)\) weakly induced by \(D\) is connected, where \(E_w\) is the set of all edges with at least one vertex in \(D\).
Magdalena Lemańska, Agnieszka Patyk
doaj  

Making a Dominating Set of a Graph Connected

Discussiones Mathematicae Graph Theory, 2018
Let G = (V,E) be a graph and S ⊆ V. We say that S is a dominating set of G, if each vertex in V \ S has a neighbor in S. Moreover, we say that S is a connected (respectively, 2-edge connected or 2-connected) dominating set of G if G[S] is connected ...
Li Hengzhe, Wu Baoyindureng, Yang Weihua
doaj   +1 more source

Computing locating-total domination number in some rotationally symmetric graphs

Science Progress, 2021
Let G = ( V , E ) be a connected graph. A locating-total dominating set in a graph G is a total dominating set S of a G , for every pair of vertices i , j ∈ V ( G ) ∖ S , such that N ( i ) ∩ S ≠ N ( j ) ∩ S .
Hassan Raza, Naveed Iqbal, Hamda Khan, Thongchai Botmart   +3 more
doaj   +1 more source

Total Domination Multisubdivision Number of a Graph

Discussiones Mathematicae Graph Theory, 2015
The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G.
Avella-Alaminos Diana, Dettlaff Magda, Lemańska Magdalena, Zuazua Rita   +3 more
doaj   +1 more source

Hn-Domination in Graphs

مجلة بغداد للعلوم, 2019
The aim of this article is to introduce a new definition of domination number in graphs called hn-domination number denoted by . This paper presents some properties which show the concepts of connected and independent hn-domination.
Omran et al.
doaj   +1 more source