Mixed domination and 2-independence in trees

Abstract

We investigate some relationships between two vastly studied parameters of a simple graph $G$. These parameters include mixed domination number (denoted by $\gamma_m(G)$) and 2-independence number ($\beta_2(G)$). For a tree $T$, we obtain $\frac{3}{4}\beta_2(T)\ge \gamma_m(T)$ and characterized all those trees which attain the equality.

Keywords

• mixed dominating function
• mixed domination number
• 2-independent set
• 2-independence number