scholarly journals -Tuple Total Restrained Domination in Complementary Prisms

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Adel P. Kazemi
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Restrained Domination ◽  
Minimum Number ◽  
Total Restrained Domination ◽  
Complementary Prism ◽  
Total Restrained Domination Number ◽  
Restrained Domination Number

In a graph with , a -tuple total restrained dominating set is a subset of such that each vertex of   is adjacent to at least vertices of and also each vertex of is adjacent to at least vertices of  . The minimum number of vertices of such sets in is the -tuple total restrained domination number of . In [-tuple total restrained domination/domatic in graphs, BIMS], the author initiated the study of the -tuple total restrained domination number in graphs. In this paper, we continue it in the complementary prism of a graph.

Critical concepts of restrained domination in signed graphs

2021 ◽  
pp. 2250010
Author(s):  
Anisha Jean Mathias ◽  
V. Sangeetha ◽  
Mukti Acharya
Keyword(s):  
Undirected Graph ◽  
Dominating Set ◽  
Domination Number ◽  
Signed Graph ◽  
Signed Graphs ◽  
Minimum Cardinality ◽  
Underlying Graph ◽  
Restrained Domination ◽  
Edge Removal ◽  
Restrained Domination Number

A signed graph [Formula: see text] is a simple undirected graph in which each edge is either positive or negative. Restrained dominating set [Formula: see text] in [Formula: see text] is a restrained dominating set of the underlying graph [Formula: see text] where the subgraph induced by the edges across [Formula: see text] and within [Formula: see text] is balanced. The minimum cardinality of a restrained dominating set of [Formula: see text] is called the restrained domination number, denoted by [Formula: see text]. In this paper, we initiate the study on various critical concepts to investigate the effect of edge removal or edge addition on restrained domination number in signed graphs.

scholarly journals Restrained domination in signed graphs

2020 ◽  
Vol 12 (1) ◽  
pp. 155-163
Author(s):  
Anisha Jean Mathias ◽  
V. Sangeetha ◽  
Mukti Acharya
Keyword(s):  
Social Networks ◽  
Dominating Set ◽  
Domination Number ◽  
Important Application ◽  
Signed Graph ◽  
Signed Graphs ◽  
Underlying Graph ◽  
Restrained Domination ◽  
Restrained Domination Number

AbstractA signed graph Σ is a graph with positive or negative signs attatched to each of its edges. A signed graph Σ is balanced if each of its cycles has an even number of negative edges. Restrained dominating set D in Σ is a restrained dominating set of its underlying graph where the subgraph induced by the edges across Σ[D : V \ D] and within V \ D is balanced. The set D having least cardinality is called minimum restrained dominating set and its cardinality is the restrained domination number of Σ denoted by γr(Σ). The ability to communicate rapidly within the network is an important application of domination in social networks. The main aim of this paper is to initiate a study on restrained domination in the realm of different classes of signed graphs.

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