scholarly journals Protection of a network by complete secure domination

2022 ◽  
pp. 53-61
Author(s):  
Girish V. RAJASEKHARAİAH ◽  
Usha P. MURTHY ◽  
Umesh SUBRAMANYA
Keyword(s):  
Secure Domination

Efficient Secure Domination in Graphs

2015 ◽  
Vol 5 (2) ◽  
pp. 59 ◽  
Author(s):  
P. Roushini Leely Pushpam ◽  
Suseendran Chitra
Keyword(s):  
Domination In Graphs ◽  
Secure Domination

scholarly journals On the Secure Domination of Benes Networks

2021 ◽  
Vol 1770 (1) ◽  
pp. 012084
Author(s):  
D Angel ◽  
R Mary Jeya Jothi ◽  
R Revathi ◽  
A. Raja
Keyword(s):  
Benes Networks ◽  
Secure Domination

Secure domination in cographs

2019 ◽  
Vol 262 ◽  
pp. 179-184 ◽  
Author(s):  
Toru Araki ◽  
Ryo Yamanaka
Keyword(s):  
Secure Domination

A simple algorithm for secure domination in proper interval graphs

2019 ◽  
Vol 260 ◽  
pp. 289-293 ◽  
Author(s):  
Y.H. Zou ◽  
J.J. Liu ◽  
C.C. Hsu ◽  
Y.L. Wang
Keyword(s):  
Simple Algorithm ◽  
Interval Graphs ◽  
Secure Domination

On secure domination in trees

2017 ◽  
Vol 40 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Zepeng Li ◽  
Zehui Shao ◽  
Jin Xu
Keyword(s):  
Secure Domination

scholarly journals Edge stability in secure graph domination

2015 ◽  
Vol Vol. 17 no. 1 (Graph Theory) ◽  
Author(s):  
Anton Pierre Burger ◽  
Alewyn Petrus Villiers ◽  
Jan Harm Vuuren
Keyword(s):  
Graph Theory ◽  
Dominating Set ◽  
Domination Number ◽  
Arbitrary Subset ◽  
Graph Domination ◽  
Vertex Set ◽  
International Audience ◽  
Edge Stability ◽  
Secure Domination

Graph Theory International audience A subset X of the vertex set of a graph G is a secure dominating set of G if X is a dominating set of G and if, for each vertex u not in X, there is a neighbouring vertex v of u in X such that the swap set (X-v)∪u is again a dominating set of G. The secure domination number of G is the cardinality of a smallest secure dominating set of G. A graph G is p-stable if the largest arbitrary subset of edges whose removal from G does not increase the secure domination number of the resulting graph, has cardinality p. In this paper we study the problem of computing p-stable graphs for all admissible values of p and determine the exact values of p for which members of various infinite classes of graphs are p-stable. We also consider the problem of determining analytically the largest value ωn of p for which a graph of order n can be p-stable. We conjecture that ωn=n-2 and motivate this conjecture.

The secure domination problem in cographs

2019 ◽  
Vol 145 ◽  
pp. 30-38 ◽  
Author(s):  
Anupriya Jha ◽  
D. Pradhan ◽  
S. Banerjee
Keyword(s):  
Domination Problem ◽  
Secure Domination

scholarly journals Secure w-Domination in Graphs

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1948
Author(s):  
Abel Cabrera Martínez ◽  
Alejandro Estrada-Moreno ◽  
Juan A. Rodríguez-Velázquez
Keyword(s):  
Open Neighborhood ◽  
Minimum Weight ◽  
Domination Number ◽  
Domination In Graphs ◽  
Secure Domination ◽  
Dominating Function

This paper introduces a general approach to the idea of protection of graphs, which encompasses the known variants of secure domination and introduces new ones. Specifically, we introduce the study of secure w-domination in graphs, where w=(w0,w1,…,wl) is a vector of nonnegative integers such that w0≥1. The secure w-domination number is defined as follows. Let G be a graph and N(v) the open neighborhood of v∈V(G). We say that a function f:V(G)⟶{0,1,…,l} is a w-dominating function if f(N(v))=∑u∈N(v)f(u)≥wi for every vertex v with f(v)=i. The weight of f is defined to be ω(f)=∑v∈V(G)f(v). Given a w-dominating function f and any pair of adjacent vertices v,u∈V(G) with f(v)=0 and f(u)>0, the function fu→v is defined by fu→v(v)=1, fu→v(u)=f(u)−1 and fu→v(x)=f(x) for every x∈V(G)\{u,v}. We say that a w-dominating function f is a secure w-dominating function if for every v with f(v)=0, there exists u∈N(v) such that f(u)>0 and fu→v is a w-dominating function as well. The secure w-domination number of G, denoted by γws(G), is the minimum weight among all secure w-dominating functions. This paper provides fundamental results on γws(G) and raises the challenge of conducting a detailed study of the topic.

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