On cubic rainbow domination regular graphs
Year: 2025
Type: article
Abstract: A $d$-regular graph $X$ is called $d$-rainbow domination regular or $d$-RDR, if its $d$-rainbow domination number $γ_{rd}(X)$ attains the lower bound $n/2$ for $d$-regular graphs, where $n$ is the number of vertices. In the paper, two combinatorial constructions to construct new $d$-RDR graphs from existing ones are described and two general criteria for a vertex-transitive $d$-regular graph to be $d$-RDR are proven. A list of vertex-transitive 3-RDR graphs of small orders is produced and their partial classification into families of generalized Petersen graphs, honeycomb-toroidal graphs and a specific family of Cayley graphs is given by investigating the girth and local cycle structure of these graphs.
Source: Discrete Applied Mathematics
Author: Boštjan Kuzman
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Awards: Distance-regular graphs: irreducible T-modules with endpoint 1 and action of the automorphism group, Semiregular elements in 2-closures of solvable groups, Symmetries in graphs via rigid cells, Terwilliger algebra of a graph, Designing certain perfect discrete combinatorial objects in spectral domain, Hamilton cycles with rotational symmetry in connected vertex-transitive graphs, Algebra, discrete mathematics, probability and game theory
OpenAlex ID: W4409754244