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Graphs with equal secure total domination and inverse secure total domination numbers
Journal of Information and Optimization Sciences, 2018AbstractA secure total dominating set of a graph G = (V, E) is a total dominating set D ⊆ V(G) with the property that for each u ∈ V(G) – D, there exists v ∈ D adjacent to u such that (D – {v}) ∪ {u} is a total dominating set. If V(G) – D contains a secure total dominating set D´ of G, then D´ is called an inverse secure total dominating set with ...
M. Kumara, B. Chaluvaraju, V. R. Kulli
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Total Domination Edge Critical Graphs with Total Domination Number Three and Many Dominating Pairs
Graphs and Combinatorics, 2014A graph $$G$$G is diameter-2-critical if its diameter is two and the deletion of any edge increases the diameter. Murty and Simon conjectured that the number of edges in a diameter-2-critical graph $$G$$G of order $$n$$n is at most $$\lfloor n^2/4 \rfloor $$?n2/4? and that the extremal graphs are the complete bipartite graphs $$K_{{\lfloor n/2 \rfloor }
Balbuena, Camino +3 more
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Relating the Size and Total Domination Number [PDF]
, 2013 In the metadata of the chapter that will be visualized online, please make the following change: “In this chapter, we determine the maximum size of a graph with given order and total domination number”
Anders Yeo, Michael A. Henning
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Signed Total Domination Nnumber of a Graph
Czechoslovak Mathematical Journal, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Essential upper bounds on the total domination number
Discrete Applied Mathematics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Algorithms for Computing Domination and Total Domination Numbers of RNPCG
Advances in Nonlinear Variational InequalitiesIntroduction: This paper presents an efficient algorithmic framework for computing the domination number (γ) and total domination number (γt) of graphs, with a focus on applications in collaboration networks. Using a greedy approach combined with minimality verification, the algorithm identifies dominating and total dominating sets that optimize ...
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