ALL libraries (COBIB.SI union bibliographic/catalogue database)
PDF
  • Double Roman graphs in P(3k,k) [Elektronski vir]
    Shao, Zehui ...
    A double Roman dominating function on a graph G=(V,E) is a function f:V->{0,1,2,3} with the properties that if f(u)=0, then vertex u is adjacent to at least one vertex assigned 3 or at least two ... vertices assigned 2, and if f(u)=1, then vertex u is adjacent to at least one vertex assigned 2 or 3. The weight of f equals w(f)=[sum]v[is an element of]Vf(v). The double Roman domination number [gamma]dR(G) of a graph G is the minimum weight of a double Roman dominating function of G. A graph is said to be double Roman if [gamma]dR(G)=3[gamma](G), where [gamma](G) is the domination number of G. We obtain the sharp lower bound of the double Roman domination number of generalized Petersen graphs P(3k,k), and we construct solutions providing the upper bounds, which gives exact values of the double Roman domination number for all generalized Petersen graphs P(3k,k). This implies that P(3k,k) is a double Roman graph if and only if either k[identical to]0 (mod 3) or k[is an element of]{1,4}.
    Source: Mathematics [Elektronski vir]. - ISSN 2227-7390 (Vol. 9, iss. 4, Feb. 2021, f. 1-18)
    Type of material - e-article
    Publish date - 2021
    Language - english
    COBISS.SI-ID - 50563587

    Link(s):

    https://www.mdpi.com/2227-7390/9/4/336
    Repository of the University of Ljubljana – RUL
    DOI

Shelf entry