\([1,2]\)-sets in graphs

DOI10.1016/j.dam.2013.06.012zbMath1287.05098OpenAlexW2093490754MaRDI QIDQ2446878

Stephen T. Hedetniemi, Teresa W. Haynes, Alice A. McRae, Mustapha Chellali

Publication date: 23 April 2014

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

Full work available at URL: https://doi.org/10.1016/j.dam.2013.06.012

zbMATH Keywords

grid graphsrestrained domination\([1, 2\)-sets]

Mathematics Subject Classification ID

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

Related Items (28)

Total \([1,2\)-domination in graphs] ⋮ \((1, j)\)-set problem in graphs ⋮ Quasiperfect domination in trees ⋮ On independent \([1, 2\)-sets in trees] ⋮ [1,2-Complementary connected domination number of graphs-III] ⋮ \([1,2\)-domination in graphs] ⋮ When an optimal dominating set with given constraints exists ⋮ A note on bipartite graphs whose [1,k-domination number equal to their number of vertices] ⋮ \([1,2\)-sets and \([1,2]\)-total sets in trees with algorithms] ⋮ On the \([1,2\)-domination number of generalized Petersen graphs] ⋮ Perfect Italian domination on planar and regular graphs ⋮ Some modified types of pitchfork domination and it's inverse ⋮ \([1,k\)-domination number of lexicographic products of graphs] ⋮ Domination cover number of graphs ⋮ New parameter of inverse domination in graphs ⋮ Parameterized complexity of minimum membership dominating set ⋮ Irregular independence and irregular domination ⋮ On the parameterized complexity of \([1,j\)-domination problems] ⋮ An explicit construction of optimal dominating and [1, 2–dominating sets in grid] ⋮ Unnamed Item ⋮ Pitchfork domination in graphs ⋮ On the Parameterized Complexity of [1,j-Domination Problems] ⋮ [1,2-Domination in generalized Petersen graphs] ⋮ On perfect and quasiperfect dominations in graphs ⋮ On \([j, k\)-sets in graphs] ⋮ Captive domination in graphs ⋮ Doubly connected bi-domination in graphs ⋮ Linear programming formulation for some generalized domination parameters

Cites Work

• Fair domination in graphs
• On domination and independent domination numbers of a graph
• Fast decoding of quasi-perfect Lee distance codes
• The weighted perfect domination problem
• Restrained domination in graphs
• Efficient dominating sets in Cayley graphs.
• Nearly perfect sets in graphs
• A generalization of Lee codes
• Perfect codes in graphs
• Graph-theoretic parameters concerning domination, independence, and irredundance
• Perfect domination in rectangular grid graphs
• Graph Classes: A Survey
• Quasiperfect domination in triangular lattices
• Perfect domination in regular grid graphs
• Perfect Codes in the Lee Metric and the Packing of Polyominoes
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