A variation of distance domination in composite networks

2021 ◽  
Author(s):  
Vecdi Aytaç ◽  
Fatmana Şentürk
Keyword(s):  
Distance Domination

scholarly journals Distance domination of generalized de Bruijn and Kautz digraphs

2016 ◽  
Vol 12 (2) ◽  
pp. 339-357
Author(s):  
Yanxia Dong ◽  
Erfang Shan ◽  
Xiao Min
Keyword(s):  
Kautz Digraphs ◽  
De Bruijn ◽  
Distance Domination

scholarly journals Distance Domination and Distance Irredundance in Graphs

10.37236/953 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Adriana Hansberg ◽  
Dirk Meierling ◽  
Lutz Volkmann
Keyword(s):  
Lower Bounds ◽  
Connected Graph ◽  
Dominating Set ◽  
Domination Number ◽  
Dominating Sets ◽  
Minimum Cardinality ◽  
Distance Domination

A set $D\subseteq V$ of vertices is said to be a (connected) distance $k$-dominating set of $G$ if the distance between each vertex $u\in V-D$ and $D$ is at most $k$ (and $D$ induces a connected graph in $G$). The minimum cardinality of a (connected) distance $k$-dominating set in $G$ is the (connected) distance $k$-domination number of $G$, denoted by $\gamma_k(G)$ ($\gamma_k^c(G)$, respectively). The set $D$ is defined to be a total $k$-dominating set of $G$ if every vertex in $V$ is within distance $k$ from some vertex of $D$ other than itself. The minimum cardinality among all total $k$-dominating sets of $G$ is called the total $k$-domination number of $G$ and is denoted by $\gamma_k^t(G)$. For $x\in X\subseteq V$, if $N^k[x]-N^k[X-x]\neq\emptyset$, the vertex $x$ is said to be $k$-irredundant in $X$. A set $X$ containing only $k$-irredundant vertices is called $k$-irredundant. The $k$-irredundance number of $G$, denoted by $ir_k(G)$, is the minimum cardinality taken over all maximal $k$-irredundant sets of vertices of $G$. In this paper we establish lower bounds for the distance $k$-irredundance number of graphs and trees. More precisely, we prove that ${5k+1\over 2}ir_k(G)\geq \gamma_k^c(G)+2k$ for each connected graph $G$ and $(2k+1)ir_k(T)\geq\gamma_k^c(T)+2k\geq |V|+2k-kn_1(T)$ for each tree $T=(V,E)$ with $n_1(T)$ leaves. A class of examples shows that the latter bound is sharp. The second inequality generalizes a result of Meierling and Volkmann and Cyman, Lemańska and Raczek regarding $\gamma_k$ and the first generalizes a result of Favaron and Kratsch regarding $ir_1$. Furthermore, we shall show that $\gamma_k^c(G)\leq{3k+1\over2}\gamma_k^t(G)-2k$ for each connected graph $G$, thereby generalizing a result of Favaron and Kratsch regarding $k=1$.

scholarly journals Distance domination and generalized eccentricity in graphs with given minimum degree

2019 ◽  
Vol 94 (1) ◽  
pp. 5-19 ◽  
Author(s):  
Peter Dankelmann ◽  
David J. Erwin
Keyword(s):  
Minimum Degree ◽  
Distance Domination

scholarly journals An algorithm to find two distance domination parameters in a graph

1996 ◽  
Vol 68 (1-2) ◽  
pp. 85-91 ◽  
Author(s):  
Gerd H. Fricke ◽  
Michael A. Henning ◽  
Ortrud R. Oellermann ◽  
Henda C. Swart
Keyword(s):  
Distance Domination

Graphs with equal domination and 2-distance domination numbers

2011 ◽  
Vol 31 (2) ◽  
pp. 375
Author(s):  
Joanna Raczek
Keyword(s):  
Distance Domination ◽  
Domination Numbers

Trees with the same distance domination number

2020 ◽  
Vol 15 (2) ◽  
pp. 91-96
Author(s):  
Min-Jen Jou ◽  
Jenq-Jong Lin ◽  
Qian-Yu Lin
Keyword(s):  
Domination Number ◽  
Distance Domination

scholarly journals Average distances and distance domination numbers

2009 ◽  
Vol 157 (5) ◽  
pp. 1113-1127 ◽  
Author(s):  
Fang Tian ◽  
Jun-Ming Xu
Keyword(s):  
Distance Domination ◽  
Domination Numbers

scholarly journals On the distance domination number of bipartite graphs

2020 ◽  
Vol 8 (2) ◽  
pp. 353
Author(s):  
Doost Ali Mojdeh ◽  
Seyed Reza Musawi ◽  
Esmaeil Nazari
Keyword(s):  
Domination Number ◽  
Bipartite Graphs ◽  
Distance Domination

Graphs having distance- domination number half their order

2000 ◽  
Vol 3 ◽  
pp. 1-4
Author(s):  
M FISCHERMANNAND ◽  
L VOLKMANN
Keyword(s):  
Domination Number ◽  
Distance Domination

scholarly journals Incorporating Distance Domination in Multiobjective Evolutionary Algorithm

2005 ◽  
pp. 684-689
Author(s):  
Praveen K. Tripathi ◽  
Sanghamitra Bandyopadhyay ◽  
Sankar K. Pal
Keyword(s):  
Evolutionary Algorithm ◽  
Multiobjective Evolutionary Algorithm ◽  
Distance Domination
Sign in / Sign up

Export Citation Format

Share Document