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Displaying similar documents to “Domination in graphs with few edges”

Cut-vertices and domination in graphs

Preben Dahl Vestergaard, Bohdan Zelinka (1995)

Mathematica Bohemica

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The paper studies the domatic numbers and the total domatic numbers of graphs having cut-vertices.

Radius-invariant graphs

Vojtech Bálint, Ondrej Vacek (2004)

Mathematica Bohemica

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The eccentricity e ( v ) of a vertex v is defined as the distance to a farthest vertex from v . The radius of a graph G is defined as a r ( G ) = min u ∈ V ( G ) { e ( u ) } . A graph G is radius-edge-invariant if r ( G - e ) = r ( G ) for every e ∈ E ( G ) , radius-vertex-invariant if r ( G - v ) = r ( G ) for every v ∈ V ( G ) and radius-adding-invariant if r ( G + e ) = r ( G ) for every e ∈ E ( G ¯ ) . Such classes of graphs are studied in this paper.