On the existence and on the number of \((k,l)\)-kernels in the lexicographic product of graphs

DOI10.1016/J.DISC.2007.08.078zbMath1169.05039OpenAlexW2094814356MaRDI QIDQ942091

Iwona Włoch, Waldemar Szumny, Andrezej Włoch

Publication date: 4 September 2008

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

Full work available at URL: https://doi.org/10.1016/j.disc.2007.08.078

zbMATH Keywords

countingefficient dominating setlexicographic product\((k, l)\)-kernel

Mathematics Subject Classification ID

Enumeration in graph theory (05C30) Structural characterization of families of graphs (05C75) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items (11)

The Fibonacci numbers of certain subgraphs of circulant graphs ⋮ On the existence and the number of independent (1,2)-dominating sets in the \(G\)-join of graphs ⋮ Generalized sequences and \(k\)-independent sets in graphs ⋮ On generalized Fibonacci numbers and \(k\)-distance \(K_p\)-matchings in graphs ⋮ \(k\)-kernels in \(k\)-transitive and \(k\)-quasi-transitive digraphs ⋮ A new generalization of kernels in digraphs ⋮ Fibonacci numbers in graphs with strong (1, 1, 2)-kernels ⋮ On the Fibonacci numbers of the composition of graphs ⋮ On the existence of \((k,l)\)-kernels in infinite digraphs: a survey ⋮ About \((k, l)\)-kernels, semikernels and Grundy functions in partial line digraphs ⋮ Unnamed Item

Cites Work

• On \((k,l)\)-kernels in generalized products
• Bounds on the number of vertex independent sets in a graph
• Principles of combinatorics
• A Note on Independent Sets in Trees
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