On weakly connected domination in graphs

DOI10.1016/S0012-365X(96)00233-6zbMath0871.05037OpenAlexW2158843278MaRDI QIDQ1356466

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

Publication date: 9 June 1997

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0012-365x(96)00233-6

zbMATH Keywords

boundsindependence numbertreesNP-harddominating setconnected graphneighborhoodweakly connected domination number

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35)

Related Items (22)

Dominating sets whose closed stars form spanning trees ⋮ Upper bounds for domination related parameters in graphs on surfaces ⋮ Spanning star trees in regular graphs ⋮ Constructing weakly connected dominating set for secure clustering in distributed sensor network ⋮ Unnamed Item ⋮ MAXIMAL INDEPENDENT SET, WEAKLY-CONNECTED DOMINATING SET, AND INDUCED SPANNERS IN WIRELESS AD HOC NETWORKS ⋮ A ZONAL ALGORITHM FOR CLUSTERING AN HOC NETWORKS ⋮ Some variants of perfect graphs related to the matching number, the vertex cover and the weakly connected domination number ⋮ Unnamed Item ⋮ The minimum weakly connected independent set problem: polyhedral results and branch-and-cut ⋮ Bounds relating the weakly connected domination number to the total domination number and the matching number ⋮ A self-stabilizing algorithm for constructing weakly connected minimal dominating sets ⋮ Domination-related parameters in rooted product graphs ⋮ LEARNING AUTOMATA-BASED ALGORITHMS FOR FINDING MINIMUM WEAKLY CONNECTED DOMINATING SET IN STOCHASTIC GRAPHS ⋮ Weakly connected domination stable trees ⋮ Connected Domination ⋮ Connected domination of regular graphs ⋮ Weakly Connected Domination in Graphs ⋮ Weakly connected Roman domination in graphs ⋮ On minimum weakly connected independent sets for wireless sensor networks: properties and enumeration algorithm ⋮ On weakly connected domination in graphs. II. ⋮ Testing equality under the local broadcast model

Cites Work

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• On domination and independent domination numbers of a graph
• Contributions to the theory of domination, independence and irredundance in graphs
• Dominating sets whose closed stars form spanning trees
• Using maximality and minimality conditions to construct inequality chains
• On Hadwiger's Number and the Stability Number
• Two Bounds for the Domination Number of a Graph

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