@article{Cabrera-Martínez2022, 
author = {Abel Cabrera-Martínez and Andrea Conchado Peiró},
title = {On the    {  2  }-domination number of graphs},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {6},
pages = {10731-10743},
keywords = {{2}-domination, double domination, total domination, w-domination},
url = {https://www.sciopen.com/article/10.3934/math.2022599},
doi = {10.3934/math.2022599},
abstract = {Let    G be a nontrivial graph and    k  ≥  1 an integer. Given a vector of nonnegative integers    w  =  (      w    0    ,  …  ,      w    k    ), a function    f  :  V  (  G  )  →  {  0  ,  …  ,  k  } is a    w-dominating function on    G if    f  (  N  (  v  )  )  ≥      w    i   for every    v  ∈  V  (  G  ) such that    f  (  v  )  =  i. The    w-domination number of    G, denoted by        γ          w        (  G  ), is the minimum weight    ω  (  f  )  =      ∑          v      ∈      V      (      G      )        f  (  v  ) among all    w-dominating functions on    G. In particular, the    {  2  }-domination number of a graph    G is defined as        γ          {      2      }        (  G  )  =      γ          (      2      ,      1      ,      0      )        (  G  ). In this paper we continue with the study of the    {  2  }-domination number of graphs. In particular, we obtain new tight bounds on this parameter and provide closed formulas for some specific families of graphs.}
}