Odd and residue domination numbers of a graph

• Volume: 21, Issue: 1, page 119-136
• ISSN: 2083-5892

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Abstract

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Let G = (V,E) be a simple, undirected graph. A set of vertices D is called an odd dominating set if |N[v] ∩ D| ≡ 1 (mod 2) for every vertex v ∈ V(G). The minimum cardinality of an odd dominating set is called the odd domination number of G, denoted by γ₁(G). In this paper, several algorithmic and structural results are presented on this parameter for grids, complements of powers of cycles, and other graph classes as well as for more general forms of "residue" domination.

How to cite

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Yair Caro, William F. Klostermeyer, and John L. Goldwasser. "Odd and residue domination numbers of a graph." Discussiones Mathematicae Graph Theory 21.1 (2001): 119-136. <http://eudml.org/doc/270762>.

@article{YairCaro2001,
abstract = {Let G = (V,E) be a simple, undirected graph. A set of vertices D is called an odd dominating set if |N[v] ∩ D| ≡ 1 (mod 2) for every vertex v ∈ V(G). The minimum cardinality of an odd dominating set is called the odd domination number of G, denoted by γ₁(G). In this paper, several algorithmic and structural results are presented on this parameter for grids, complements of powers of cycles, and other graph classes as well as for more general forms of "residue" domination.},
author = {Yair Caro, William F. Klostermeyer, John L. Goldwasser},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {dominating set; odd dominating set; parity domination},
language = {eng},
number = {1},
pages = {119-136},
title = {Odd and residue domination numbers of a graph},
url = {http://eudml.org/doc/270762},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Yair Caro
AU - William F. Klostermeyer
AU - John L. Goldwasser
TI - Odd and residue domination numbers of a graph
JO - Discussiones Mathematicae Graph Theory
PY - 2001
VL - 21
IS - 1
SP - 119
EP - 136
AB - Let G = (V,E) be a simple, undirected graph. A set of vertices D is called an odd dominating set if |N[v] ∩ D| ≡ 1 (mod 2) for every vertex v ∈ V(G). The minimum cardinality of an odd dominating set is called the odd domination number of G, denoted by γ₁(G). In this paper, several algorithmic and structural results are presented on this parameter for grids, complements of powers of cycles, and other graph classes as well as for more general forms of "residue" domination.
LA - eng
KW - dominating set; odd dominating set; parity domination
UR - http://eudml.org/doc/270762
ER -

References

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