scholarly journals Strong Dominating Sets of Lexicographic Product Graph of Cayley Graphs with Arithmetic Graphs

2013 ◽  
Vol 6 (6) ◽  
pp. 25-29
Author(s):  
M. Manjuri ◽  
B. Maheswari
Keyword(s):  
Cayley Graphs ◽  
Lexicographic Product ◽  
Dominating Sets ◽  
Product Graph

scholarly journals Efficient dominating sets in Cayley graphs

2003 ◽  
Vol 129 (2-3) ◽  
pp. 319-328 ◽  
Author(s):  
Italo J. Dejter ◽  
Oriol Serra
Keyword(s):  
Cayley Graphs ◽  
Dominating Sets

Antimagic Labeling of the Lexicographic Product Graph $$K_{m,n}[P_k]$$ K m , n [ P k ]

2017 ◽  
Vol 12 (1) ◽  
pp. 77-90 ◽  
Author(s):  
Yingyu Lu ◽  
Guanghua Dong ◽  
Wenhui Ma ◽  
Ning Wang
Keyword(s):  
Lexicographic Product ◽  
Product Graph ◽  
Antimagic Labeling

scholarly journals On Resolving Hop Domination in Graphs

2021 ◽  
Vol 14 (3) ◽  
pp. 1015-1023
Author(s):  
Jerson Saguin Mohamad ◽  
Helen M. Rara
Keyword(s):  
Connected Graph ◽  
Dominating Set ◽  
Domination Number ◽  
Lexicographic Product ◽  
Dominating Sets ◽  
Resolving Set ◽  
Domination In Graphs

A set S of vertices in a connected graph G is a resolving hop dominating set of G if S is a resolving set in G and for every vertex v ∈ V (G) \ S there exists u ∈ S such that dG(u, v) = 2. The smallest cardinality of such a set S is called the resolving hop domination number of G. This paper presents the characterizations of the resolving hop dominating sets in the join, corona and lexicographic product of two graphs and determines the exact values of their corresponding resolving hop domination number.

scholarly journals Dominating sets in Cayley graphs on $ Z_{n} $

2007 ◽  
Vol 38 (4) ◽  
pp. 341-345 ◽  
Author(s):  
T. Tamizh Chelvam ◽  
I. Rani
Keyword(s):  
Cayley Graph ◽  
Cayley Graphs ◽  
Dominating Set ◽  
Domination Number ◽  
Dominating Sets ◽  
Generating Set ◽  
Minimal Dominating Set

A Cayley graph is a graph constructed out of a group $ \Gamma $ and its generating set $ A $. In this paper we attempt to find dominating sets in Cayley graphs constructed out of $ Z_{n} $. Actually we find the value of domination number for $ Cay(Z_{n}, A) $ and a minimal dominating set when $ |A| $ is even and further we have proved that $ Cay(Z_{n}, A) $ is excellent. We have also shown that $ Cay(Z_{n}, A) $ is $ 2- $excellent, when $ n = t(|A|+1)+1 $ for some integer $ t, t>0 $.

scholarly journals Forcing Subsets for γc-sets and γt-sets in the Lexicographic Product of Graphs

2019 ◽  
Vol 12 (4) ◽  
pp. 1779-1786
Author(s):  
Cris Laquibla Armada ◽  
Sergio, Jr. R. Canoy ◽  
Carmelito E. Go
Keyword(s):  
Total Domination ◽  
Lexicographic Product ◽  
Dominating Sets ◽  
Connected Dominating Sets ◽  
Product Of Graphs ◽  
Domination Numbers

In this paper, the connected dominating sets and total dominating sets in the lexicographic product of two graphs are characterized. Further, the connected domination, total domination, forcing connected domination and forcing total domination numbers of these graphs are determined.

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