Maximum sizes of graphs with given domination parameters

DOI10.1016/j.disc.2003.07.010zbMath1044.05053OpenAlexW2166264712MaRDI QIDQ1827704

Henda C. Swart, Johannes H. Hattingh, Peter Dankelmann, P. J. P. Grobler, Gayla S. Domke, Wayne Goddard

Publication date: 6 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.disc.2003.07.010

zbMATH Keywords

extremal graphssizedominationirredundancetotal dominationindependent domination

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items

Equality in a bound that relates the size and the restrained domination number of a graph ⋮ Maximum size of digraphs with some parameters ⋮ On size, order, diameter and minimum degree ⋮ Some spin glass ideas applied to the clique problem ⋮ Optimal linear‐Vizing relationships for (total) domination in graphs ⋮ Unnamed Item ⋮ Equality in a linear Vizing-like relation that relates the size and total domination number of a graph ⋮ Graphs with maximum size and given paired-domination number ⋮ On size, order, diameter and edge-connectivity of graphs ⋮ A survey of selected recent results on total domination in graphs ⋮ An inequality that relates the size of a bipartite graph with its order and restrained domination number ⋮ Relating the size of a connected graph to its total and restricted domination numbers ⋮ Bounds on neighborhood total domination number in graphs

Cites Work

• Maximum number of edges in connected graphs with a given domination number
• A generalization of Vizing's theorem on domination
• Star forests, dominating sets and Ramsey-type problems
• On the number of edges in graphs with a given connected domination number
• Total domination in graphs
• A linear vizing-like relation between the size and the domination number of a graph
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