Full domination in graphs

Robert C. Brigham; Gary Chartrand; Ronald D. Dutton; Ping Zhang

Discussiones Mathematicae Graph Theory (2001)

  • Volume: 21, Issue: 1, page 43-62
  • ISSN: 2083-5892

Abstract

top
For each vertex v in a graph G, let there be associated a subgraph H v of G. The vertex v is said to dominate H v as well as dominate each vertex and edge of H v . A set S of vertices of G is called a full dominating set if every vertex of G is dominated by some vertex of S, as is every edge of G. The minimum cardinality of a full dominating set of G is its full domination number γ F H ( G ) . A full dominating set of G of cardinality γ F H ( G ) is called a γ F H -set of G. We study three types of full domination in graphs: full star domination, where H v is the maximum star centered at v, full closed domination, where H v is the subgraph induced by the closed neighborhood of v, and full open domination, where H v is the subgraph induced by the open neighborhood of v.

How to cite

top

Robert C. Brigham, et al. "Full domination in graphs." Discussiones Mathematicae Graph Theory 21.1 (2001): 43-62. <http://eudml.org/doc/270252>.

@article{RobertC2001,
abstract = {For each vertex v in a graph G, let there be associated a subgraph $H_v$ of G. The vertex v is said to dominate $H_v$ as well as dominate each vertex and edge of $H_v$. A set S of vertices of G is called a full dominating set if every vertex of G is dominated by some vertex of S, as is every edge of G. The minimum cardinality of a full dominating set of G is its full domination number $γ_\{FH\}(G)$. A full dominating set of G of cardinality $γ_\{FH\}(G)$ is called a $γ_\{FH\}$-set of G. We study three types of full domination in graphs: full star domination, where $H_v$ is the maximum star centered at v, full closed domination, where $H_v$ is the subgraph induced by the closed neighborhood of v, and full open domination, where $H_v$ is the subgraph induced by the open neighborhood of v.},
author = {Robert C. Brigham, Gary Chartrand, Ronald D. Dutton, Ping Zhang},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {full domination; full star domination; full closed domination; full open domination; full domination number; full star domination number; full closed domination number; full open domination number},
language = {eng},
number = {1},
pages = {43-62},
title = {Full domination in graphs},
url = {http://eudml.org/doc/270252},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Robert C. Brigham
AU - Gary Chartrand
AU - Ronald D. Dutton
AU - Ping Zhang
TI - Full domination in graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2001
VL - 21
IS - 1
SP - 43
EP - 62
AB - For each vertex v in a graph G, let there be associated a subgraph $H_v$ of G. The vertex v is said to dominate $H_v$ as well as dominate each vertex and edge of $H_v$. A set S of vertices of G is called a full dominating set if every vertex of G is dominated by some vertex of S, as is every edge of G. The minimum cardinality of a full dominating set of G is its full domination number $γ_{FH}(G)$. A full dominating set of G of cardinality $γ_{FH}(G)$ is called a $γ_{FH}$-set of G. We study three types of full domination in graphs: full star domination, where $H_v$ is the maximum star centered at v, full closed domination, where $H_v$ is the subgraph induced by the closed neighborhood of v, and full open domination, where $H_v$ is the subgraph induced by the open neighborhood of v.
LA - eng
KW - full domination; full star domination; full closed domination; full open domination; full domination number; full star domination number; full closed domination number; full open domination number
UR - http://eudml.org/doc/270252
ER -

References

top
  1. [1] T. Gallai, Über extreme Punkt- und Kantenmengen, Ann. Univ. Sci. Budapest, Eötvös Sect. Math. 2 (1959) 133-138. 
  2. [2] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). Zbl0890.05002
  3. [3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998). Zbl0883.00011
  4. [4] S.R. Jayaram, Y.H.H. Kwong and H.J. Straight, Neighborhood sets in graphs, Indian J. Pure Appl. Math. 22 (1991) 259-268. Zbl0733.05074
  5. [5] E. Sampathkumar and P.S. Neeralagi, The neighborhood number of a graph, Indian J. Pure Appl. Math. 16 (1985) 126-136. Zbl0564.05052
  6. [6] O. Ore, Theory of Graphs, Amer. Math. Soc. Colloq. Publ. 38 (Amer. Math. Soc. Providence, RI, 1962). 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.