scholarly journals Upper bounds for inverse domination in graphs

2021 ◽  
Vol 8 (2) ◽  
pp. 1-9
Author(s):  
Elliot Krop ◽  
◽  
Jessica McDonald ◽  
Gregory J. Puleo ◽  
◽  
...  
Keyword(s):  
Upper Bounds ◽  
Domination In Graphs

scholarly journals On restricted domination in graphs

2007 ◽  
Vol 57 (5) ◽  
Author(s):  
Vladimir Samodivkin
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Upper Bounds ◽  
Minimum Number ◽  
Domination In Graphs ◽  
Restricted Domination Number

AbstractThe k-restricted domination number of a graph G is the minimum number d k such that for any subset U of k vertices of G, there is a dominating set in G including U and having at most d k vertices. Some new upper bounds in terms of order and degrees for this number are found.

scholarly journals Further Results on the Total Roman Domination in Graphs

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 349 ◽  
Author(s):  
Abel Cabrera Martínez ◽  
Suitberto Cabrera García ◽  
Andrés Carrión García
Keyword(s):  
Lower Bound ◽  
Necessary Conditions ◽  
Minimum Weight ◽  
Domination Number ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Roman Domination ◽  
Roman Domination Number ◽  
Roman Dominating Function ◽  
Domination In Graphs

Let G be a graph without isolated vertices. A function f : V ( G ) → { 0 , 1 , 2 } is a total Roman dominating function on G if every vertex v ∈ V ( G ) for which f ( v ) = 0 is adjacent to at least one vertex u ∈ V ( G ) such that f ( u ) = 2 , and if the subgraph induced by the set { v ∈ V ( G ) : f ( v ) ≥ 1 } has no isolated vertices. The total Roman domination number of G, denoted γ t R ( G ) , is the minimum weight ω ( f ) = ∑ v ∈ V ( G ) f ( v ) among all total Roman dominating functions f on G. In this article we obtain new tight lower and upper bounds for γ t R ( G ) which improve the well-known bounds 2 γ ( G ) ≤ γ t R ( G ) ≤ 3 γ ( G ) , where γ ( G ) represents the classical domination number. In addition, we characterize the graphs that achieve equality in the previous lower bound and we give necessary conditions for the graphs which satisfy the equality in the upper bound above.

Captive domination in graphs

2020 ◽  
Vol 12 (06) ◽  
pp. 2050076 ◽  
Author(s):  
Manal N. Al-Harere ◽  
Ahmed A. Omran ◽  
Athraa T. Breesam
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Upper Bounds ◽  
Proper Subset ◽  
Total Domination ◽  
Lower And Upper Bounds ◽  
Graph Domination ◽  
Total Dominating Set ◽  
Definition Of ◽  
Domination In Graphs

In this paper, a new definition of graph domination called “Captive Domination” is introduced. The proper subset of the vertices of a graph [Formula: see text] is a captive dominating set if it is a total dominating set and each vertex in this set dominates at least one vertex which doesn’t belong to the dominating set. The inverse captive domination is also introduced. The lower and upper bounds for the number of edges of the graph are presented by using the captive domination number. Moreover, the lower and upper bounds for the captive domination number are found by using the number of vertices. The condition when the total domination and captive domination number are equal to two is discussed and obtained results. The captive domination in complement graphs is discussed. Finally, the captive dominating set of paths and cycles are determined.

scholarly journals Randomized algorithms and upper bounds for multiple domination in graphs and networks

2013 ◽  
Vol 161 (4-5) ◽  
pp. 604-611 ◽  
Author(s):  
Andrei Gagarin ◽  
Anush Poghosyan ◽  
Vadim Zverovich
Keyword(s):  
Randomized Algorithms ◽  
Upper Bounds ◽  
Graphs And Networks ◽  
Domination In Graphs

Generalization of the total outer-connected domination in graphs

2016 ◽  
Vol 50 (2) ◽  
pp. 233-239
Author(s):  
Nader Jafari Rad ◽  
Lutz Volkmann
Keyword(s):  
Domination In Graphs

Equitable Cototal Domination in Graphs

2012 ◽  
Vol 3 (7) ◽  
pp. 301-305
Author(s):  
Dr. B. Basavanagoud Dr. B. Basavanagoud ◽  
◽  
Vijay V Teli
Keyword(s):  
Domination In Graphs

RESTRAINED LICT DOMINATION IN GRAPHS

2014 ◽  
Vol 03 (05) ◽  
pp. 784-790 ◽  
Author(s):  
M.H. Muddebihal .
Keyword(s):  
Domination In Graphs

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Total Complementary Acyclic Domination in Graphs

2013 ◽  
Vol 3 (2) ◽  
pp. 5
Author(s):  
M. Valliammal ◽  
S. P. Subbiah ◽  
V. Swaminathan
Keyword(s):  
Domination In Graphs
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