On the $ \{2\} $-domination number of graphs

• DOI: 10.3934/math.2022599
• Publication Date: 2022-03-31T10:51:58Z
• Authors: Abel Cabrera-Mart...; Andrea Conchado P...
• Keywords: Domination analysis

<abstract><p>Let $ G be a nontrivial graph and k\geq 1 an integer. Given vector of nonnegative integers w = (w_0, \ldots, w_k) $, function f: V(G)\rightarrow \{0, k\} is $-dominating on if f(N(v))\geq w_i for every v\in V(G) such that f(v) i $. The $-domination number denoted by \gamma_{w}(G) the minimum weight \omega(f) \sum_{v\in V(G)}f(v) among all functions In particular, \{2\} defined as \gamma_{\{2\}}(G) \gamma_{(2, 1, 0)}(G) this paper we continue with study graphs. obtain new tight bounds parameter provide closed formulas some specific families graphs.</p></abstract>