@techreport{TR-IC-25-01,
   number = {IC-25-01},
   author = {A. A. {Pereira} and C. N. {Campos}},
   title  =  {{The  domination  and  independent domination numbers of
                   Goldberg Graphs}},
   month = {October},
   year = {2025},
   institution = {Institute of Computing, University of Campinas},
   note = {In English, 13 pages.
    \par\selectlanguage{english}\textbf{Abstract}
       A  dominating set of a graph $G$ is a subset $S \subseteq V(G)$
       such  that  every  vertex in $V(G)$ either belongs to $S$ or is
       adjacent   to   some  vertex  in  $S$.  The  domination  number 
       $\gamma(G)$  is  the minimum cardinality of a dominating set of
       $G$.  An  independent dominating set of $G$ is a dominating set
       that  is  also  independent  and  $i(G)$  is the cardinality of
       minimum  independent  dominating  set of $G$. The computational
       complexity  of  these  problems  has  led to extensive research
       focused  on  establishing  bounds  or  exact  values  for these
       parameters  in  for  graph  families,  especially cubic graphs.
       Additionally,  determining the gap between these two parameters
       is  a  challenging problem. In this work, we introduce a family
       of   cubic   graphs,   called   Goldberg  Graphs  $G_l$,  which 
       generalizes  the  well-known Goldberg Snarks and show that, for
       these graphs, $\gamma(G_l) = i(G_l) = \left\lceil \frac{11l}{5}
       \right\rceil$.
  }
}