# Algorithmic aspects of total-subdomination in graphs

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

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## Abstract

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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.

## How to cite

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Laura 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 -

## References

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