scholarly journals On the Power Domination Number of de Bruijn and Kautz Digraphs

2018 ◽  
pp. 264-272 ◽  
Author(s):  
Cyriac Grigorious ◽  
Thomas Kalinowski ◽  
Sudeep Stephen
Keyword(s):  
Domination Number ◽  
Power Domination ◽  
Kautz Digraphs ◽  
De Bruijn

ON THE TWIN DOMINATION NUMBER IN GENERALIZED DE BRUIJN AND GENERALIZED KAUTZ DIGRAPHS

2010 ◽  
Vol 02 (02) ◽  
pp. 199-205 ◽  
Author(s):  
JYHMIN KUO
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Kautz Digraphs ◽  
De Bruijn ◽  
Kautz Digraph ◽  
De Bruijn Digraph ◽  
Domination Numbers

Let V and A denote the vertex and edge sets of a digraph G. A set T ⊆V is a twin dominating set of G if for every vertex v ∈ V - T, there exist u, w ∈ T (possibly u = w) such that arcs (u, v), (v, w) ∈ A. The twin domination number γ*(G) of G is the cardinality of a minimum twin dominating set of G. In this note, we investigate the twin domination numbers of generalized de Bruijn digraph and generalized Kautz digraph. The bounds of twin domination number of special generalized Kautz digraphs are given.

Power domination in generalized undirected de Bruijn graphs and Kautz graphs

2015 ◽  
Vol 07 (01) ◽  
pp. 1550003 ◽  
Author(s):  
Jyhmin Kuo ◽  
Wei-Lun Wu
Keyword(s):  
Power System ◽  
Dominating Set ◽  
Vertex Cover ◽  
Domination Number ◽  
Electric Power System ◽  
Minimum Cardinality ◽  
Power Domination ◽  
De Bruijn Graphs ◽  
De Bruijn ◽  
Kautz Graphs

To monitor an electric power system by placing as few phase measurement units (PMUs) as possible is closely related to the famous vertex cover problem and domination problem in graph theory. A set P is a power dominating set (PDS) of a graph G = (V, E), if every vertex and every edge in the system is observed following the observation rules of power system monitoring. The minimum cardinality of a PDS of a graph G is the power domination number γp(G). In this paper, we determine the upper bounds of power domination number of generalized undirected de Bruijn graphs and generalized undirected Kautz graphs.

scholarly journals Study on power domination number of some classes of graphs

2020 ◽  
Author(s):  
T. N. Saibavani ◽  
N. Parvathi
Keyword(s):  
Domination Number ◽  
Power 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 Layer structure of De Bruijn and Kautz digraphs. An application to deflection routing

2016 ◽  
Vol 54 ◽  
pp. 157-162
Author(s):  
J. Fàbrega ◽  
J. Martí-Farré ◽  
X. Muñoz
Keyword(s):  
Layer Structure ◽  
Deflection Routing ◽  
Kautz Digraphs ◽  
De Bruijn

scholarly journals Equitable power domination number of total graph of certain graphs

2020 ◽  
Vol 1531 ◽  
pp. 012073
Author(s):  
S Banu Priya ◽  
A Parthiban ◽  
P Abirami
Keyword(s):  
Domination Number ◽  
Total Graph ◽  
Power Domination

Power domination number of sunlet graph and other graphs

2019 ◽  
Vol 22 (6) ◽  
pp. 1121-1127
Author(s):  
T. N. Saibavani ◽  
N. Parvathi
Keyword(s):  
Domination Number ◽  
Power Domination

scholarly journals Heredity for generalized power domination

2016 ◽  
Vol Vol. 18 no. 3 (Graph Theory) ◽  
Author(s):  
Paul Dorbec ◽  
Seethu Varghese ◽  
Ambat Vijayakumar
Keyword(s):  
Domination Number ◽  
Power Domination ◽  
Edge Contraction ◽  
Vertex Deletion ◽  
International Audience ◽  
Optimal Bounds

International audience In this paper, we study the behaviour of the generalized power domination number of a graph by small changes on the graph, namely edge and vertex deletion and edge contraction. We prove optimal bounds for $\gamma_{p,k}(G-e)$, $\gamma_{p,k}(G/e)$ and for $\gamma_{p,k}(G-v)$ in terms of $\gamma_{p,k}(G)$, and give examples for which these bounds are tight. We characterize all graphs for which $\gamma_{p,k}(G-e) = \gamma_{p,k}(G)+1$ for any edge $e$. We also consider the behaviour of the propagation radius of graphs by similar modifications.

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