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On perfect and quasiperfect dominations in graphs

Author
Hernando, M.; Mora, M.; Pelayo, I. M.; Cáceres, José; Puertas, M. Luz
Type of activity
Journal article
Journal
Filomat
Date of publication
2017-02-27
Volume
31
Number
2
First page
413
Last page
423
DOI
10.2298 / FIL1702413C
Project funding
Morfología geométrica computacional.
Repository
http://hdl.handle.net/2117/104244 Open in new window
URL
http://www.pmf.ni.ac.rs/pmf/publikacije/filomat/2017/31-2/31-2-20-2080.pdf Open in new window
Abstract
A subset S ¿ V in a graph G = ( V , E ) is a k -quasiperfect dominating set (for k = 1) if every vertex not in S is adjacent to at least one and at most k vertices in S . The cardinality of a minimum k -quasiperfect dominating set in G is denoted by ¿ 1 k ( G ). Those sets were first introduced by Chellali et al. (2013) as a generalization of the perfect domination concept and allow us to construct a decreasing chain of quasiperfect dominating numbers n = ¿ 11 ( G ) = ¿ 12 ( G ) = ... = ¿ 1...
Citation
Hernando, M., Mora, M., Pelayo, I. M., Cáceres, José, Puertas, M. L. On perfect and quasiperfect dominations in graphs. "Filomat", 27 Febrer 2017, vol. 31, núm. 2, p. 413-423.
Keywords
Domination, claw-free graphs, cograph, perfect domination, quasiperfect domination
Group of research
COMBGRAPH - Combinatorics, Graph Theory and Applications
DCG - Discrete and Combinatorial Geometry

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