Some results on global dominating sets

Vaidya, S. K.; Pandit, R. M.

doi:10.4067/s0716-09172013000300003

Proyecciones (Antofagasta)

2013

DOI: 10.4067/s0716-09172013000300003

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Some results on global dominating sets

S. K. Vaidya

R. M. Pandit²

Abstract: A dominating set is called a global dominating set if it is a dominating set for a graph G and its complement G. We investigate some general results for global dominating sets corresponding to the graphs P n , C n and W n .

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2023

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The forcing geodetic global domination number of a graph

Selvi¹,

Flower

2023

Discrete Math. Algorithm. Appl.

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Let [Formula: see text] be a connected graph and [Formula: see text] be a minimum geodetic global dominating set of [Formula: see text]. A subset [Formula: see text] is called a forcing subset for [Formula: see text] if [Formula: see text] is the unique minimum geodetic global dominating set containing [Formula: see text]. A forcing subset for [Formula: see text] of minimum cardinality is a minimum forcing subset of [Formula: see text]. The forcing geodetic global domination number of [Formula: see text], denoted by [Formula: see text], is the cardinality of a minimum forcing subset of S. The forcing geodetic global domination number of [Formula: see text], denoted by [Formula: see text], is [Formula: see text], where the minimum is taken over all minimum geodetic global dominating sets [Formula: see text] in [Formula: see text]. The forcing geodetic global domination number of some standard graphs are determined. Some of its general properties are studied. It is shown that for every pair of positive integers a and b with [Formula: see text] and [Formula: see text], there exists a connected graph [Formula: see text] such that [Formula: see text] and [Formula: see text]. The geodetic global domination number of join of graphs is also studied. Connected graphs of order [Formula: see text] with geodetic global domination number 2 are characterized. It is proved that, for a connected graph [Formula: see text] with [Formula: see text]. Then [Formula: see text] and characterized connected graphs for which the lower and the upper bounds are sharp.

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The forcing geodetic global domination number of a graph

Selvi¹,

Flower

2023

Discrete Math. Algorithm. Appl.

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Some results on global dominating sets

Abstract: A dominating set is called a global dominating set if it is a dominating set for a graph G and its complement G. We investigate some general results for global dominating sets corresponding to the graphs P n , C n and W n .

Cited by 1 publication

References 3 publications

The forcing geodetic global domination number of a graph

The forcing geodetic global domination number of a graph

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