Displaying similar documents to “Locally connected graphs”

On the doubly connected domination number of a graph

Joanna Cyman, Magdalena Lemańska, Joanna Raczek (2006)

Open Mathematics

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For a given connected graph G = (V, E), a set D ⊆ V ( G ) 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.

The vertex monophonic number of a graph

A.P. Santhakumaran, P. Titus (2012)

Discussiones Mathematicae Graph Theory

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For a connected graph G of order p ≥ 2 and a vertex x of G, a set S ⊆ V(G) is an x-monophonic set of G if each vertex v ∈ V(G) lies on an x -y monophonic path for some element y in S. The minimum cardinality of an x-monophonic set of G is defined as the x-monophonic number of G, denoted by mₓ(G). An x-monophonic set of cardinality mₓ(G) is called a mₓ-set of G. We determine bounds for it and characterize graphs which realize these bounds. A connected graph of order p with vertex monophonic...