Concepedia

Geodetic Domination in Graphs

Adriana Hansberg, Henry Escuadro, Ralucca Gera, Lutz Volkmann, N. Rad Jafari

2011 · 18 citations · 6 references

Concepts

Abstract

A subset S of vertices in a graph G is a called a geodetic dominating set if S is both a geodetic set and a (standard) dominating set. In this paper, we study geodetic domination on graphs.

References

6

A linear algorithm for the domination number of a tree

E. J. Cockayne, S. E. Goodman, Stephen T. Hedetniemi · Information Processing Letters · 1975 · 190 citations

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On the geodetic number of a graph

Gary Chartrand, Frank Harary, Ping Zhang · Networks · 2001 · 177 citations

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Geodetic sets in graphs

Gary Chartrand, Frank Harary, Ping Zhang · Discussiones Mathematicae Graph Theory · 2000 · 59 citations · Full text

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Extremal results on the geodetic number of a graph

Fred Buckley, F. Harary, Louis V. Quintas · 1988 · 41 citations

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Upper bounds on the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>k</mml:mi></mml:math>-domination number and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" display="inline" overflow="scroll"><mml:mi>k</mml:mi></mml:math>-Roman domination number

Adriana Hansberg, Lutz Volkmann · Discrete Applied Mathematics · 2008 · 39 citations

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