Authors: Kratica, Jozef 
Matić, Dragan
Filipović, Vladimir
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Weakly convex and convex domination numbers for generalized Petersen and flower snark graphs
Journal: Revista de la Unión Matemática Argentina
Volume: 61
Issue: 2
First page: 441
Last page: 455
Issue Date: 2020
Rank: M23
ISSN: 0041-6932
DOI: 10.33044/revuma.v61n2a16
We consider the weakly convex and convex domination numbers for two classes of graphs: generalized Petersen graphs and flower snark graphs. For a given generalized Petersen graph GP(n,k), we prove that if k=1 and n≥4 then both the weakly convex domination number γwcon(GP(n,k)) and the convex domination number γcon(GP(n,k)) are equal to n. For k≥2 and n≥13, γwcon(GP(n,k))=γcon(GP(n,k))=2n, which is the order of GP(n,k). Special cases for smaller graphs are solved by the exact method. For a flower snark graph Jn, where n is odd and n≥5, we prove that γwcon(Jn)=2n and γcon(Jn)=4n.
Publisher: Unión Matemática Argentina
Project: Mathematical Modelas and Optimization Methods on Large-Scale Systems 
Graph theory and mathematical programming with applications in chemistry and computer science 

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