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New Upper Bounds on the Distance Domination
In March 2013, by Fata, Smith and Sundaram established upper bounds for the k-distance domination numbers of grid graphs by generalizing Chang's construction of dominating sets to k-distance dominating sets.
File link: http://web.unlv.edu/misc/mcccc/28/abstracts/Grez.pdf
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Go To Link - New Upper Bounds on the Distance Domination
The independent domination number of | 2 Upper bounds
In this section, we present an upper bound on the independent domination number of an MTF graph in terms of its minimum degree and then its order. Advanced Topics, Marcel Dekker, New York, 1998. [10] P.C.B. Lam, W.C. Shiu and L. Sun, On independent domination number of.
File link: http://ajc.maths.uq.edu.au/pdf/42/ajc_v42_p129.pdf
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Go To Link - The independent domination number of | 2 Upper bounds
Independent Domination in Graphs: A Survey | 2.1 General Bounds
Extremal graphs for a new upper bound on domination parameters in graphs. Discrete Math., 306:2314-2326, 2006. A bound on the independent domination number of a tree. Vishwa Internat. J. Graph Theory, 1:19-27, 1992.
File link: https://people.cs.clemson.edu/~goddard/papers/idomSurvey.pdf
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Go To Link - Independent Domination in Graphs: A Survey | 2.1 General Bounds
Characterization of Two Domination Number and
In this paper, we obtain sharp upper bound for the sum of the two domination number and chromatic number and characterize the corresponding extremal graphs. In all the above cases, it can be verified that no new graph exists.
File link: http://www.ripublication.com/irph/ijcsm/IJCSMv3n2_10.pdf
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Go To Link - Characterization of Two Domination Number and
Upper Bounds for α -Domination Parameters
We provide a new upper bound for the α-domination number in terms of a parameter α, 0 < α ≤ 1, and graph vertex degrees. This result generalises the well-known Caro-Roditty bound for the domination number of a graph.
File link: http://www.cems.uwe.ac.uk...Domination Parameters.pdf
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An upper bound on the total
We prove the following upper bound on the total outer-independent domination number of a tree. [4] T. Haynes, S. Hedetniemi, P. Slater (eds.), Domination in Graphs: Advanced Topics, Marcel Dekker, New York, 1998.
File link: http://www.opuscula.agh.edu.pl/vol32/1/art/opuscula_math_3212.pdf
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Go To Link - An upper bound on the total
Bounds on the k -Domination Number of a Graph
We prove two bounds on the k-domination number of a graph, inspired by two conjectures of the computer program Grati.pc. In particular, we show that for any graph with minimum degree at least 2k − 1, the k-domination number is at most the matching number.
File link: https://people.cs.clemson.edu/~goddard/papers/kDomination.pdf
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Go To Link - Bounds on the k -Domination Number of a Graph
Domination number and chromatic | Fuzzy Graph G
Fuzzy double domination number and chromatic number of a fuzzy graph. an upper bound for the sum of the Fuzzy Double Domination Number and Chromatic Number in fuzzy graphs and characterize. For all the remaining cases, no new graph exits.
File link: http://www.csjournals.com/IJITKM/PDF 4-2/Article_32.pdf
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Go To Link - Domination number and chromatic | Fuzzy Graph G
Minimal dominating sets
The independent domination number Other domination parameters. Graph-Theory 9. 10. 11.3. Bounds on the Domination Number. Using the above theorem we have an upper bound for (G) in terms of the order of G.
File link: http://www.iwr.uni-heidel...theory/graph-theory-9.pdf
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The 4/5 Upper Bound on the
Applying Theorem 18 to the resulting colored-graph G, we have that γtg(G) ≤ 4n/5. To prove the upper bound on the Staller-start game total domination number, we [9] T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York, 1998.
File link: https://www.fmf.uni-lj.si...Dom_Upper_Bound_final.pdf
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Go To Link - The 4/5 Upper Bound on the