Conditional resolvability in graphs: a survey.
Saenpholphat, Varaporn, Zhang, Ping (2004)
International Journal of Mathematics and Mathematical Sciences
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Saenpholphat, Varaporn, Zhang, Ping (2004)
International Journal of Mathematics and Mathematical Sciences
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Bohdan Zelinka (1986)
Mathematica Slovaca
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Chengfu Qin, Xiaofeng Guo, Weihua Yang (2013)
Czechoslovak Mathematical Journal
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An edge of a -connected graph is said to be -removable if is still -connected. A subgraph of a -connected graph is said to be -contractible if its contraction results still in a -connected graph. A -connected graph with neither removable edge nor contractible subgraph is said to be minor minimally -connected. In this paper, we show that there is a contractible subgraph in a -connected graph which contains a vertex who is not contained in any triangles. Hence, every vertex...
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.