Weakly convex and convex domination numbers for generalized Petersen and flower snark graphs

Jozef Kratica ^[1] ; Dragan Matic ^[2] ; Vladimir Filipovic ^[3]
1. [1] Serbian Academy of Sciences and Arts
  
  Serbian Academy of Sciences and Arts
  
  Serbia
2. [2] University of Banja Luka
  
  University of Banja Luka
  
  Bosnia y Herzegovina
3. [3] University of Belgrade
  
  University of Belgrade
  
  Serbia
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Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 61, Nº. 2, 2020, págs. 441-455
Idioma: inglés
DOI: 10.33044/revuma.v61n2a16
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Resumen
- 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.