Characterisation of Restrained Domination Number and Chromatic Number of a Fuzzy Graph

2014 ◽  
Vol 11 (2) ◽  
pp. 117-123
Author(s):  
J.S Sathya ◽  
◽  
S Vimala
Keyword(s):  
Chromatic Number ◽  
Domination Number ◽  
Fuzzy Graph ◽  
Restrained Domination ◽  
Restrained Domination Number

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 -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.

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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