On cubic rainbow domination regular graphs

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.

Keywords

dominacija rednih grafov;posplošeni Petersenovi grafi;toroidni grafi medenih satov;rainbow domination regular graphs;generalized Petersen graphs;honeycomb toroidal graphs;cubic vertex-transitive graphs;

Data

Language:	English
Year of publishing:	2025
Typology:	1.01 - Original Scientific Article
Organization:	UL PEF - Faculty of Education
UDC:	519.17
COBISS:	234771971
ISSN:	1872-6771
Views:	39
Downloads:	26
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	dominacija rednih grafov;posplošeni Petersenovi grafi;toroidni grafi medenih satov;
Type (COBISS):	Article
Pages:	str. 26-38
Issue:	ǂVol. ǂ373
Chronology:	2025
DOI:	10.1016/j.dam.2025.04.046
ID:	26347861