On weakly connected domination in graphs

Dunbar, Jean E.; Grossman, Jerrold W.; Hattingh, Johannes H.; Hedetniemi, Stephen T.; McRae, Alice A.

doi:10.1016/s0012-365x(96)00233-6

Cited by 62 publications

(34 citation statements)

References 5 publications

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“…, E w ) (also called subgraph weakly induced by D) is connected, where E w is the set of all edges having at least one vertex in D. Dunbar et al [6] defined the weakly connected domination number γ w (G) of a graph G to be the minimum cardinality among all weakly connected dominating sets in G.…”

Section: Weakly Connected Domination Numbermentioning

confidence: 99%

Domination-Related Parameters in Rooted Product Graphs

Kuziak

Lemańska

Yero

2015

Bull. Malays. Math. Sci. Soc.

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Section: Weakly Connected Domination Numbermentioning

confidence: 99%

Domination-Related Parameters in Rooted Product Graphs

Kuziak

Lemańska

Yero

2015

Bull. Malays. Math. Sci. Soc.

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“…In [1], Dunbar, et al, showed that every connected graph has a weakly connected independent dominating set. Thus, the i w (G) and β w (G) of a connected graph G always exist.…”

Section: Introductionmentioning

confidence: 99%

Weakly connected independent domination in the join of graphs

Leonida¹

2013

imf

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“…To reduce the number of exchanged SYNC frames while maintaining the network connected, we structure it according to a Weakly Connected Dominating Set (WCDS) [6]. A WCDS is composed of independent clusters that can use different virtual channels for internal communication, which only requires maintaining synchronization inside one cluster.…”

Section: Introductionmentioning

confidence: 99%

Energy Efficient Network Structure for Synchronous Preamble Sampling in Wireless Sensor Networks

Théoleyre

Bachir

Chakchouk

et al. 2010

2010 IEEE International Conference on Communications

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Abstract-We propose a new energy efficient network structure for maintaining synchronization in access methods based on Synchronous Preamble Sampling. Our scheme limits the number of synchronization messages and increases network capacity through the use of multiple non-interfering virtual channels. It consists in constructing independent clusters based on the Weakly Connected Dominating Set (WCDS) so that clusters can use different virtual channels and only need to maintain internal synchronization, while still offering global connectivity. We define a distributed and self-stabilizing algorithm for constructing and maintaining the clusters. Our simulation results show that the proposed scheme has comparable energy consumption as Scheduled Channel Polling, but results in better network capacity. Moreover, it achieves better energy savings and network capacity than recently proposed Crankshaft access method.

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On weakly connected domination in graphs

Cited by 62 publications

References 5 publications

Domination-Related Parameters in Rooted Product Graphs

Domination-Related Parameters in Rooted Product Graphs

Weakly connected independent domination in the join of graphs

Energy Efficient Network Structure for Synchronous Preamble Sampling in Wireless Sensor Networks

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