We settle two conjectures on domination-search, a game proposed by Fomin et.al. [1], one in affirmative and the other in negative. The two results presented here are (1) domination search number can be greater than domination-target number, (2) domination search number for asteroidal-triple-free graphs is at most 2.

MacGillivray and Seyffarth (J. Graph Theory 22 (1996), 213–229) proved that planar graphs of diameter three have domination number at most ten. Recently it was shown (J. Graph Theory 40 (2002), 1–25) that a planar graph of diameter three and of radius two has domination number at most six while every sufficiently large planar graph of diameter three has domination number at most seven. In this ...

This note considers the problem of global stabilization by output feedback, for a family of nonlinear systems that are dominated by a triangular system satisfying linear growth condition. The problem has remained unsolved due to the violation of the commonly assumed conditions in the literature. Using a feedback domination design method which is not based on the separation principle, we explici...

We consider four different types of multiple domination and provide new improved upper bounds for the kand k-tuple domination numbers. They generalise two classical bounds for the domination number and are better than a number of known upper bounds for these two multiple domination parameters. Also, we explicitly present and systematize randomized algorithms for finding multiple dominating sets...

An exact lower bound for the domination number and the total domination number of the direct product of finitely many complete graphs is given: (×i=1Kni) ≥ t + 1, t ≥ 3. Sharpness is established in the case when the factors are large enough in comparison to the number of factors. The main result gives a lower bound for the domination (and the total domination) number of the direct product of tw...

Domination is a relation between general operations defined on a poset. The old open problem is whether domination is transitive on the set of all t-norms. In this paper we contribute partially by inspection of domination in the family of Frank and Hamacher tnorms. We show that between two different t-norms from the same family, the domination occurs iff at least one of the t-norms involved is ...

This paper studies the problem of disturbance attenuation with internal stability via output feedback for a family of nonlinear systems. Using a feedback domination design which substantially differs from the separation principle, we explicitly construct a dynamic output compensator attenuating the disturbance’s effect on the output to an arbitrary degree of accuracy in the L2-gain sense, and a...

let $d=(v,a)$ be a finite simple directed graph. a function$f:vlongrightarrow {-1,0,1}$ is called a twin minus dominatingfunction (tmdf) if $f(n^-[v])ge 1$ and $f(n^+[v])ge 1$ for eachvertex $vin v$. the twin minus domination number of $d$ is$gamma_{-}^*(d)=min{w(f)mid f mbox{ is a tmdf of } d}$. inthis paper, we initiate the study of twin minus domination numbersin digraphs and present some lo...

KENT BUSE AND ANDREW HARMER ABSTRACT Ken Buse and Andrew Harmer review the political dimensions of global public–private health partnerships through the ‘three faces of power’ lens. They attempt to answer the questions: who has power; how is power exercised; and on what basis? Evidence, although scant, suggests that a northern elite wields power through its domination of governing bodies and al...