Displaying similar documents to “Domination numbers on the Boolean function graph of a graph”

Domination numbers on the complement of the Boolean function graph of a graph

T. N. Janakiraman, S. Muthammai, M. Bhanumathi (2005)

Mathematica Bohemica

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For any graph G , let V ( G ) and E ( G ) denote the vertex set and the edge set of G respectively. The Boolean function graph B ( G , L ( G ) , N I N C ) of G is a graph with vertex set V ( G ) ∪ E ( G ) and two vertices in B ( G , L ( G ) , N I N C ) are adjacent if and only if they correspond to two adjacent vertices of G , two adjacent edges of G or to a vertex and an edge not incident to it in G . For brevity, this graph is denoted by B 1 ( G ) . In this paper, we determine domination number, independent, connected, total, point-set, restrained, split and non-split domination...

Global domination and neighborhood numbers in Boolean function graph of a graph

T. N. Janakiraman, S. Muthammai, M. Bhanumathi (2005)

Mathematica Bohemica

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For any graph G , let V ( G ) and E ( G ) denote the vertex set and the edge set of G respectively. The Boolean function graph B ( G , L ( G ) , N I N C ) of G is a graph with vertex set V ( G ) ∪ E ( G ) and two vertices in B ( G , L ( G ) , N I N C ) are adjacent if and only if they correspond to two adjacent vertices of G , two adjacent edges of G or to a vertex and an edge not incident to it in G . In this paper, global domination number, total global domination number, global point-set domination number and neighborhood number for this graph are obtained. ...

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.