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 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

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.

scholarly journals Note on power propagation time and lower bounds for the power domination number

2016 ◽  
Vol 34 (3) ◽  
pp. 736-741 ◽  
Author(s):  
Daniela Ferrero ◽  
Leslie Hogben ◽  
Franklin H. J. Kenter ◽  
Michael Young
Keyword(s):  
Lower Bounds ◽  
Domination Number ◽  
Propagation Time ◽  
Power Domination

scholarly journals Forcing Subsets for γ∗ tpw -sets in Graphs

2021 ◽  
Vol 14 (2) ◽  
pp. 451-470
Author(s):  
Cris Laquibla Armada
Keyword(s):  
Domination Number ◽  
Upper Bounds ◽  
Complete Graphs ◽  
Lower And Upper Bounds ◽  
Power Domination ◽  
Wheel Graphs

In this paper, the lower and upper bounds of the forcing total dr-power dominationnumber of any graph are determined. Total dr-power domination number of some special graphs such as complete graphs, star, fan and wheel graphs are shown. Moreover, the forcing total dr-power domination number of these graphs, together with paths and cycles, are determined.

scholarly journals Power Domination Number On Shackle Operation with Points as Lingkage

2020 ◽  
Vol 4 (1) ◽  
pp. 1
Author(s):  
Ilham Saifudin
Keyword(s):  
Mathematical Logic ◽  
Maximum Degree ◽  
Nearest Neighbor ◽  
Dominating Set ◽  
Domination Number ◽  
Axiomatic Method ◽  
Star Graph ◽  
Power Domination ◽  
Path Graph ◽  
Deductive Method

The Power dominating set is a minimum point of determination in a graph that can dominate the connected dots around it, with a minimum domination point. The smallest cardinality of a power dominating set is called a power domination number with the notation . The purpose of this study is to determine the Shackle operations graph value from several special graphs with a point as a link. The result operation graphs are: Shackle operation graph from Path graph , Shackle operation graph from Sikel graph , Shackle operation graph from Star graph . The method used in this paper is axiomatic deductive method in solving problems. Understanding the axiomatic method itself is a method of deductive proof principles that applies in mathematical logic by using theorems that already exist in solving a problem. In this paper begins by determining the paper object that is the Shackle point operations result graph. Next, determine the cardinality of these graphs. After that, determine the point that has the maximum degree on the graph as the dominator point of power domination. Then, check whether the nearest neighbor has two or more degrees and analyze its optimization by using a ceiling function comparison between zero forching with the greatest degree of graph. Thus it can be determined ϒp minimal and dominated. The results of the power domination number study on Shackle operation graph result with points as connectors are , for  and ; , for  and ; , for  and .

scholarly journals Power domination in splitting and degree splitting graph

2021 ◽  
Vol 40 (6) ◽  
pp. 1641-1655
Author(s):  
J. Anitha ◽  
S. Muthukumar
Keyword(s):  
Dominating Set ◽  
Power Grid ◽  
Domination Number ◽  
Power Domination ◽  
Grid Monitoring ◽  
Vertex Set ◽  
Splitting Graph

A vertex set S is called a power dominating set of a graph G if every vertex within the system is monitored by the set S following a collection of rules for power grid monitoring. The power domination number of G is the order of a minimal power dominating set of G. In this paper, we solve the power domination number for splitting and degree splitting graph.

scholarly journals Forcing Total dr-Power Domination Number of Graphs Under Some Binary Operations

2021 ◽  
Vol 14 (3) ◽  
pp. 1098-1107
Author(s):  
Cris Laquibla Armada
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Domination Number ◽  
Lexicographic Product ◽  
Power Domination ◽  
Binary Operations ◽  
Product Of Graphs

In this paper, the total dr-power domination number of graphs such as complete bipartite graph, generalized fan and generalized wheel are obtained. The forcing total dr-power domination number of graphs resulting from some binary operations such as join, corona and lexicographic product of graphs were determined.

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