Location-domatic number of a graph

Bohdan Zelinka

Mathematica Bohemica (1998)

  • Volume: 123, Issue: 1, page 67-71
  • ISSN: 0862-7959

Abstract

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A subset D of the vertex set V ( G ) of a graph G is called locating-dominating, if for each x V ( G ) - D there exists a vertex y D adjacent to x and for any two distinct vertices x 1 , x 2 of V ( G ) - D the intersections of D with the neighbourhoods of x 1 and x 2 are distinct. The maximum number of classes of a partition of V ( G ) whose classes are locating-dominating sets in G is called the location-domatic number of G . Its basic properties are studied.

How to cite

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Zelinka, Bohdan. "Location-domatic number of a graph." Mathematica Bohemica 123.1 (1998): 67-71. <http://eudml.org/doc/248302>.

@article{Zelinka1998,
abstract = {A subset $D$ of the vertex set $V(G)$ of a graph $G$ is called locating-dominating, if for each $x\in V(G)-D$ there exists a vertex $y\rightarrow D$ adjacent to $x$ and for any two distinct vertices $x_1$, $x_2$ of $V(G)-D$ the intersections of $D$ with the neighbourhoods of $x_1$ and $x_2$ are distinct. The maximum number of classes of a partition of $V(G)$ whose classes are locating-dominating sets in $G$ is called the location-domatic number of $G.$ Its basic properties are studied.},
author = {Zelinka, Bohdan},
journal = {Mathematica Bohemica},
keywords = {locating-dominating set; location-domatic partition; location-domatic number; domatic number; locating-dominating set; location-domatic partition; location-domatic number; domatic number},
language = {eng},
number = {1},
pages = {67-71},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Location-domatic number of a graph},
url = {http://eudml.org/doc/248302},
volume = {123},
year = {1998},
}

TY - JOUR
AU - Zelinka, Bohdan
TI - Location-domatic number of a graph
JO - Mathematica Bohemica
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 123
IS - 1
SP - 67
EP - 71
AB - A subset $D$ of the vertex set $V(G)$ of a graph $G$ is called locating-dominating, if for each $x\in V(G)-D$ there exists a vertex $y\rightarrow D$ adjacent to $x$ and for any two distinct vertices $x_1$, $x_2$ of $V(G)-D$ the intersections of $D$ with the neighbourhoods of $x_1$ and $x_2$ are distinct. The maximum number of classes of a partition of $V(G)$ whose classes are locating-dominating sets in $G$ is called the location-domatic number of $G.$ Its basic properties are studied.
LA - eng
KW - locating-dominating set; location-domatic partition; location-domatic number; domatic number; locating-dominating set; location-domatic partition; location-domatic number; domatic number
UR - http://eudml.org/doc/248302
ER -

References

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  1. E. J. Cockayne S. T. Hedetniemi, 10.1002/net.3230070305, Networks 7 (1977), 247-261. (1977) MR0483788DOI10.1002/net.3230070305
  2. D. F. Rall P. J. Slater, On location-domination numbers for certain classes of graphs, Congressus Numerantium 45 (1984), 77-106. (1984) MR0777715

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