Alternating connectivity of digraphs
Bohdan Zelinka (1971)
Časopis pro pěstování matematiky
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Bohdan Zelinka (1971)
Časopis pro pěstování matematiky
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Hartmann, Sven, Little, C.H.C. (2005)
The Electronic Journal of Combinatorics [electronic only]
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Wenjing Li, Xueliang Li, Jingshu Zhang (2018)
Discussiones Mathematicae Graph Theory
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A path in a vertex-colored graph is called vertex-rainbow if its internal vertices have pairwise distinct colors. A vertex-colored graph G is rainbow vertex-connected if for any two distinct vertices of G, there is a vertex-rainbow path connecting them. For a connected graph G, the rainbow vertex-connection number of G, denoted by rvc(G), is defined as the minimum number of colors that are required to make G rainbow vertex-connected. In this paper, we find all the families ℱ of connected...
Bohdan Zelinka (1975)
Czechoslovak Mathematical Journal
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Bohdan Zelinka (1981)
Časopis pro pěstování matematiky
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Joanna Cyman, Magdalena Lemańska, Joanna Raczek (2006)
Open Mathematics
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For a given connected graph G = (V, E), a set is a doubly connected dominating set if it is dominating and both 〈D〉 and 〈V (G)-D〉 are connected. The cardinality of the minimum doubly connected dominating set in G is the doubly connected domination number. We investigate several properties of doubly connected dominating sets and give some bounds on the doubly connected domination number.