Upper bounds on the upper signed total domination number of graphs

Authors:
Erfang Shan;T. C. E. Cheng
Affiliations:
Department of Mathematics, Shanghai University, Shanghai 200444, PR China and Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 1
Cited 1

Signed domination in regular graphs and set-systems

Journal of Combinatorial Theory Series B

On the complexity of signed and minus total domination in graphs

Information Processing Letters

Quantified Score

Hi-index	0.04

Visualization

Abstract

Let G=(V,E) be a graph. A function f:V-{-1,+1} defined on the vertices of G is a signed total dominating function if the sum of its function values over any open neighborhood is at least one. A signed total dominating function f is minimal if there does not exist a signed total dominating function g, fg, for which g(v)@?f(v) for every v@?V. The weight of a signed total dominating function is the sum of its function values over all vertices of G. The upper signed total domination number of G is the maximum weight of a minimal signed total dominating function on G. In this paper we present a sharp upper bound on the upper signed total domination number of an arbitrary graph. This result generalizes previous results for regular graphs and nearly regular graphs.