Total $k$-distance domination critical graphs

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 i...

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Bibliographic Details
Published in:Transactions on combinatorics 2016-09, Vol.5 (3), p.1-9
Main Authors: Doost Ali Mojdeh, A. Sayed-Khalkhali, Hossein Abdollahzadeh Ahangar, Yancai Zhao
Format: Article
Language:English
Subjects:
Distance domination
total $k$-distance dominating set
total $k$-distance domination-critical
Online Access:Get full text
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Summary: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.
ISSN:2251-8657
2251-8665