Lower bounds for the domination number and the total domination number of direct product graphs

DOI10.1016/j.disc.2010.07.015zbMath1221.05263OpenAlexW2071641257MaRDI QIDQ712256

Gašper Mekiš

Publication date: 28 October 2010

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

Full work available at URL: https://doi.org/10.1016/j.disc.2010.07.015

zbMATH Keywords

dominating setcomplete graphdomination numbertotal domination numbertotal dominating setdirect product graphs

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69) Graph operations (line graphs, products, etc.) (05C76)

Related Items (11)

Connectivity and other invariants of generalized products of graphs ⋮ Unitary Cayley graphs whose Roman domination numbers are at most four ⋮ Domination and upper domination of direct product graphs ⋮ Unnamed Item ⋮ Domination in direct products of complete graphs ⋮ On the super connectivity of Kronecker products of graphs ⋮ On the roman domination in the lexicographic product of graphs ⋮ New results on connected dominating structures in graphs ⋮ Tightness of domination inequalities for direct product graphs ⋮ Domination parameters of the unitary Cayley graph of \(\mathbb{Z}/n \mathbb{Z} \) ⋮ Classification of rings with unit graphs having domination number less than four

Cites Work

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• An almost complete description of perfect codes in direct products of cycles
• Dominating direct products of graphs
• Perfect codes in direct products of cycles-a complete characterization
• On the total domination number of cross products of graphs
• Idomatic partitions of direct products of complete graphs
• Perfect \(r\)-domination in the Kronecker product of two cycles, with an application to diagonal/toroidal mesh
• On the domination number of cross products of graphs
• On a Vizing-like conjecture for direct product graphs
• Associative graph products and their independence, domination and coloring numbers
• Total Domination in Categorical Products of Graphs
• Perfect r-domination in the Kronecker product of three cycles
• Some results on total domination in direct products of graphs

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