scholarly journals ON GRAPHS WITH PAIRWISE DISJOINT EFFICIENT DOMINATING SETS AND EFFICIENT DOMINATION IN TREES IN TERMS OF SUPPORT VERTICES

2021 ◽  
Vol 26 (1) ◽  
pp. 83-108
Author(s):  
A. Senthil Thilak ◽  
Sujatha V. Shet ◽  
S. S. Kamath
Keyword(s):  
Pairwise Disjoint ◽  
Dominating Sets

Algorithms to Compute some Dominating Sets of ES (N, K) and ESC (N, K)

2014 ◽  
Vol 4 (1) ◽  
pp. 35
Author(s):  
Pious Missier ◽  
Anto Kinsley ◽  
Evangeline Prathibha Fernando
Keyword(s):  
Dominating Sets

scholarly journals Locating and paired-dominating sets in graphs

2009 ◽  
Vol 157 (15) ◽  
pp. 3268-3280 ◽  
Author(s):  
John McCoy ◽  
Michael A. Henning
Keyword(s):  
Dominating Sets

scholarly journals Efficient enumeration of dominating sets for sparse graphs

2021 ◽  
Author(s):  
Kazuhiro Kurita ◽  
Kunihiro Wasa ◽  
Hiroki Arimura ◽  
Takeaki Uno
Keyword(s):  
Dominating Sets ◽  
Sparse Graphs

Constructing Minimum Connected Dominating Sets with Bounded Diameters in Wireless Networks

2009 ◽  
Vol 20 (2) ◽  
pp. 147-157 ◽  
Author(s):  
Donghyun Kim ◽  
Yiwei Wu ◽  
Yingshu Li ◽  
Feng Zou ◽  
Ding-Zhu Du
Keyword(s):  
Wireless Networks ◽  
Dominating Sets ◽  
Connected Dominating Sets

scholarly journals On the Number of Perfect Matchings in Random Lifts

2010 ◽  
Vol 19 (5-6) ◽  
pp. 791-817 ◽  
Author(s):  
CATHERINE GREENHILL ◽  
SVANTE JANSON ◽  
ANDRZEJ RUCIŃSKI
Keyword(s):  
Asymptotic Formula ◽  
Complete Graph ◽  
Pairwise Disjoint ◽  
Perfect Matching ◽  
Perfect Matchings ◽  
Lattice Points ◽  
Laplace’S Method ◽  
Second Moment ◽  
Multiple Dimensions ◽  
Laplace's Method

Let G be a fixed connected multigraph with no loops. A random n-lift of G is obtained by replacing each vertex of G by a set of n vertices (where these sets are pairwise disjoint) and replacing each edge by a randomly chosen perfect matching between the n-sets corresponding to the endpoints of the edge. Let XG be the number of perfect matchings in a random lift of G. We study the distribution of XG in the limit as n tends to infinity, using the small subgraph conditioning method.We present several results including an asymptotic formula for the expectation of XG when G is d-regular, d ≥ 3. The interaction of perfect matchings with short cycles in random lifts of regular multigraphs is also analysed. Partial calculations are performed for the second moment of XG, with full details given for two example multigraphs, including the complete graph K4.To assist in our calculations we provide a theorem for estimating a summation over multiple dimensions using Laplace's method. This result is phrased as a summation over lattice points, and may prove useful in future applications.

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