Displaying similar documents to “On problems related to characteristic vertices of graphs”

A metric for graphs

Vladimír Baláž, Jaroslav Koča, Vladimír Kvasnička, Milan Sekanina (1986)

Časopis pro pěstování matematiky

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On Generalized Sierpiński Graphs

Juan Alberto Rodríguez-Velázquez, Erick David Rodríguez-Bazan, Alejandro Estrada-Moreno (2017)

Discussiones Mathematicae Graph Theory

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In this paper we obtain closed formulae for several parameters of generalized Sierpiński graphs S(G, t) in terms of parameters of the base graph G. In particular, we focus on the chromatic, vertex cover, clique and domination numbers.

Supermagic Generalized Double Graphs 1

Jaroslav Ivančo (2016)

Discussiones Mathematicae Graph Theory

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A graph G is called supermagic if it admits a labelling of the edges by pairwise di erent consecutive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In this paper we will introduce some constructions of supermagic labellings of some graphs generalizing double graphs. Inter alia we show that the double graphs of regular Hamiltonian graphs and some circulant graphs are supermagic.

Eternal Domination: Criticality and Reachability

William F. Klostermeyer, Gary MacGillivray (2017)

Discussiones Mathematicae Graph Theory

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We show that for every minimum eternal dominating set, D, of a graph G and every vertex v ∈ D, there is a sequence of attacks at the vertices of G which can be defended in such a way that an eternal dominating set not containing v is reached. The study of the stronger assertion that such a set can be reached after a single attack is defended leads to the study of graphs which are critical in the sense that deleting any vertex reduces the eternal domination number. Examples of these graphs...