Superstable graphs
Heinrich Herre, Allan Mekler, Kenneth Smith (1983)
Fundamenta Mathematicae
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Heinrich Herre, Allan Mekler, Kenneth Smith (1983)
Fundamenta Mathematicae
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Levit, Vadim E., Mândrescu, Eugen (2005)
Acta Universitatis Apulensis. Mathematics - Informatics
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Mustapha Chellali, Teresa W. Haynes, Lutz Volkmann (2010)
Discussiones Mathematicae Graph Theory
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Let k be a positive integer and G = (V(G),E(G)) a graph. A subset S of V(G) is a k-independent set of G if the subgraph induced by the vertices of S has maximum degree at most k-1. The maximum cardinality of a k-independent set of G is the k-independence number βₖ(G). A graph G is called β¯ₖ-stable if βₖ(G-e) = βₖ(G) for every edge e of E(G). First we give a necessary and sufficient condition for β¯ₖ-stable graphs. Then we establish four equivalent conditions for β¯ₖ-stable trees. ...
J.L. Fouquet, H. Thuillier, J.M. Vanherpe, A.P. Wojda (2013)
Discussiones Mathematicae Graph Theory
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A graph G is a (Kq, k) stable graph (q ≥ 3) if it contains a Kq after deleting any subset of k vertices (k ≥ 0). Andrzej ˙ Zak in the paper On (Kq; k)-stable graphs, ( doi:/10.1002/jgt.21705) has proved a conjecture of Dudek, Szyma´nski and Zwonek stating that for sufficiently large k the number of edges of a minimum (Kq, k) stable graph is (2q − 3)(k + 1) and that such a graph is isomorphic to sK2q−2 + tK2q−3 where s and t are integers such that s(q − 1) + t(q − 2) − 1 = k. We have...
Alain Hertz (2000)
The Yugoslav Journal of Operations Research
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Allen, Peter, Lozin, Vadim, Rao, Michaël (2009)
The Electronic Journal of Combinatorics [electronic only]
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Hoang, C.T., Le, V.B. (2001)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Pavel Tomasta, Eliška Tomová (1988)
Czechoslovak Mathematical Journal
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Christian Barrientos, Sarah Minion (2018)
Discussiones Mathematicae Graph Theory
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When a graceful labeling of a bipartite graph places the smaller labels in one of the stable sets of the graph, it becomes an α-labeling. This is the most restrictive type of difference-vertex labeling and it is located at the very core of this research area. Here we use an extension of the adjacency matrix to count and classify α-labeled graphs according to their size, order, and boundary value.
Majid Hajian, Nader Jafari Rad (2017)
Discussiones Mathematicae Graph Theory
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A Roman dominating function (or just RDF) on a graph G = (V,E) is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of an RDF f is the value f(V (G)) = Pu2V (G) f(u). The Roman domination number of a graph G, denoted by R(G), is the minimum weight of a Roman dominating function on G. A graph G is Roman domination stable if the Roman domination number of G remains unchanged under...
Babel, Luitpold, Brandstädt, Andreas, Le, Van Bang (2002)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Klaus-Peter Podewski, Martin Ziegler (1978)
Fundamenta Mathematicae
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Gliviak, Ferdinand, Kyš, P. (1997)
Acta Mathematica Universitatis Comenianae. New Series
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