On cubic rainbow domination regular graphs

Povzetek

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.

Ključne besede

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

Podatki

Jezik:	Angleški jezik
Leto izida:	2025
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL PEF - Pedagoška fakulteta
UDK:	519.17
COBISS:	234771971
ISSN:	1872-6771
Št. ogledov:	39
Št. prenosov:	26
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Slovenski jezik
Sekundarne ključne besede:	dominacija rednih grafov;posplošeni Petersenovi grafi;toroidni grafi medenih satov;
Vrsta dela (COBISS):	Članek v reviji
Strani:	str. 26-38
Zvezek:	ǂVol. ǂ373
Čas izdaje:	2025
DOI:	10.1016/j.dam.2025.04.046
ID:	26347861