Relating the size of a connected graph to its total and restricted domination numbers

DOI10.1016/J.DISC.2003.11.011zbMath1042.05075OpenAlexW2037891560MaRDI QIDQ1827789

Laura A. Sanchis

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.2003.11.011

zbMATH Keywords

Dominating setRestricted dominationTotal domination number

Mathematics Subject Classification ID

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

Cites Work

• Some inequalities about connected domination number
• Maximum number of edges in connected graphs with a given domination number
• A generalization of Vizing's theorem on domination
• Maximum sizes of graphs with given domination parameters
• On the number of edges in graphs with a given weakly connected domination number
• On the number of edges in graphs with a given connected domination number
• Total domination in graphs
• Bounds related to domination in graphs with minimum degree two
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Related Items (8)

Upper bounds for domination related parameters in graphs on surfaces ⋮ Girth and total domination in graphs ⋮ Optimal linear‐Vizing relationships for (total) domination in graphs ⋮ 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 ⋮ Restricted domination parameters in graphs ⋮ Total domination in 2-connected graphs and in graphs with no induced 6-cycles ⋮ A survey of selected recent results on total domination in graphs

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