Total $k$-distance domination critical graphs

Document Type: Research Paper

Authors

1 University of Tafresh

2 Department of Basic Science, Babol University of Technology, Babol, I.R. Iran

3 Wuxi City College of Vocational Technology

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 within‎ ‎distance $k$ of a vertex in $S$‎. ‎A graph $G$ is total $k$-distance‎ ‎domination-critical if $\gamma_{t}^{k} (G‎ - ‎x) < \gamma_{t}^{k}‎ ‎(G)$ for any vertex $x\in V(G)$‎. ‎In this paper‎, ‎we investigate some results on total $k$-distance domination-critical of graphs‎.

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