# Algorithmic aspects of total-subdomination in graphs

Laura M. Harris; Johannes H. Hattingh; Michael A. Henning

Discussiones Mathematicae Graph Theory (2006)

- Volume: 26, Issue: 1, page 5-18
- ISSN: 2083-5892

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topLaura M. Harris, Johannes H. Hattingh, and Michael A. Henning. "Algorithmic aspects of total-subdomination in graphs." Discussiones Mathematicae Graph Theory 26.1 (2006): 5-18. <http://eudml.org/doc/270679>.

@article{LauraM2006,

abstract = {Let G = (V,E) be a graph and let k ∈ Z⁺. A total k-subdominating function is a function f: V → \{-1,1\} such that for at least k vertices v of G, the sum of the function values of f in the open neighborhood of v is positive. The total k-subdomination number of G is the minimum value of f(V) over all total k-subdominating functions f of G where f(V) denotes the sum of the function values assigned to the vertices under f. In this paper, we present a cubic time algorithm to compute the total k-subdomination number of a tree and also show that the associated decision problem is NP-complete for general graphs.},

author = {Laura M. Harris, Johannes H. Hattingh, Michael A. Henning},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {total k-subdomination; algorithm; tree; total domination; majority domination; signed domination},

language = {eng},

number = {1},

pages = {5-18},

title = {Algorithmic aspects of total-subdomination in graphs},

url = {http://eudml.org/doc/270679},

volume = {26},

year = {2006},

}

TY - JOUR

AU - Laura M. Harris

AU - Johannes H. Hattingh

AU - Michael A. Henning

TI - Algorithmic aspects of total-subdomination in graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2006

VL - 26

IS - 1

SP - 5

EP - 18

AB - Let G = (V,E) be a graph and let k ∈ Z⁺. A total k-subdominating function is a function f: V → {-1,1} such that for at least k vertices v of G, the sum of the function values of f in the open neighborhood of v is positive. The total k-subdomination number of G is the minimum value of f(V) over all total k-subdominating functions f of G where f(V) denotes the sum of the function values assigned to the vertices under f. In this paper, we present a cubic time algorithm to compute the total k-subdomination number of a tree and also show that the associated decision problem is NP-complete for general graphs.

LA - eng

KW - total k-subdomination; algorithm; tree; total domination; majority domination; signed domination

UR - http://eudml.org/doc/270679

ER -

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