Total $k$-distance domination critical graphs

Abstract

A set $S$ of vertices in a graph $G=(V,E)$ is called a total$k$-distance dominating set if every vertex in $V$ is withindistance $k$ of a vertex in $S$. A graph $G$ is total $k$-distancedomination-critical if $gamma_{t}^{k} (G - x) < gamma_{t}^{k}(G)$ for any vertex $xin V(G)$. In this paper,we investigate some results on total $k$-distance domination-critical of graphs.

Keywords

• Distance domination
• total $k$-distance dominating set
• total $k$-distance domination-critical