Results 271 to 280 of about 7,398 (287)

The connected hub number and the connected domination number

Networks, 2011
AbstractThe connected hub number hc(G) of a connected graph G is the smallest order of a connected subgraph H of G such that any two nonadjacent vertices of G − H are joined in G by a path with all internal vertices in H. Letting γc(G) denote the connected domination number of G, it is easy to see that hc(G) ≤ γc(G) ≤ hc(G) + 1 for every connected ...
Peter D. Johnson Jr., Peter Slater, Matt Walsh 0001   +2 more
openaire   +1 more source

An inequality on connected domination parameters

Ars Comb., 1998
A subset \(S\) of the vertex set \(V(G)\) of a graph \(G\) is dominating in \(G\), if each vertex of \(G\) either is in \(S\), or is adjacent to a vertex of \(S\). If moreover the subgraph of \(G\) induced by \(S\) is connected, \(S\) is called a connected dominating set in \(G\). The minimum number of vertices of a connected dominating set in \(G\) is
Hongquan Yu, Tianming Wang
openaire   +1 more source

Triple Connected Domination Number and Strong Triple Connected Domination Number of a Connected Graph

International Journal of Mathematics Trends and Technology, 2015
The concept of connectedness plays crucial role in any meshing. A variety of connectedness has been studied in the literature by considering the existence of a path between any two vertices. A communication network in which a communicating node can send a message to two stations at one stretch will be more effective and economic.
Maneesha Sakalle, Richa Jain
openaire   +1 more source

Connected Fair Domination in Graphs

2017
In this paper, we introduce the notion of connected fair domination in graphs. A connected fair dominating set in a graph G (or \(\mathsf {CFD}\)-set) is a dominating set S such that \(\langle S \rangle \) is connected in G and all vertices not in S are dominated by the same number of vertices from S, i.e., every two vertices not in S has the same ...
Angsuman Das, Wyatt J. Desormeaux
openaire   +1 more source

Connected Domination

2020
Mustapha Chellali, Odile Favaron
openaire   +1 more source

A Proof of a Conjecture on the Connected Domination Number

Bulletin of the Malaysian Mathematical Sciences Society, 2022
Saeed Kosari, S M Sheikholeslami, Mustapha Chellali   +2 more
exaly  

Disprove of a Conjecture on the Doubly Connected Domination Subdivision Number

Bulletin of the Iranian Mathematical Society, 2021
Saeed Kosari, Zehui Shao, S M Sheikholeslami   +2 more
exaly  

Every 3-connected claw-free graph with domination number at most 3 is hamiltonian-connected

Discrete Mathematics, 2022
Petr Vrana, Xingzhi Zhan
exaly  

Bounds on the connected domination number of a graph

Discrete Applied Mathematics, 2013
Wyatt J Désormeaux, Teresa W Haynes, Michael A Henning   +2 more
exaly  

On the forcing connected domination number of a graph

Journal of Discrete Mathematical Sciences and Cryptography, 2017
J John
exaly