The use of the word “eternal” in the title of Richard Horton's piece “Occupied Palestine, an eternal alliance for health” (March 30, p 1084)1 is apt. It fits with his evangelical intentions “to put science in the service of social justice and selfdetermination.”2 However, Horton omits important data, leading to the spurious conclusion that President Obama, by disappointing the Palestinians, is ...

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...

It is widely held that propositions perform a plethora of theoretical roles. They are believed to be the semantic values of sentences in contexts, the objects of attitudes, the contents of illocutionary acts, the referents of ‘that’-clauses, and the primary bearers of truth. This assumption is often combined with the claim that propositions have their truth-values eternally. Following Kaplan’s ...

Third University Department of Cardiology Aristotle University of Thessaloniki Greece e-mail: [email protected]

We argue that many future-eternal inflating spacetimes are likely to violate the weak energy condition. It is possible that such spacetimes may not enforce any of the known averaged conditions either. If this is indeed the case, it may open the door to constructing non-singular, past-eternal inflating cosmologies. Simple non-singular models are, however, unsatisfactory , and it is not clear if ...

A set S of vertices of a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S. The independent domination number of G, denoted by i(G), is the minimum cardinality of an independent dominating set of G. In this paper, some new classes of graphs with equal domination and independent domination numbers are presented and exa...

In this note, we prove several lower bounds on the domination number of simple connected graphs. Among these are the following: the domination number is at least two-thirds of the radius of the graph, three times the domination number is at least two more than the number of cut-vertices in the graph, and the domination number of a tree is at least as large as the minimum order of a maximal matc...

A graph G with no isolated vertex is total domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G− v is less than the total domination number of G. We call these graphs γt-critical. In this paper, we determine the domination and the total domination number in the Circulant graphs Cn〈1, 3〉, and then study γ-criticality...

Harary, F. , 1997 Graph Theory, Narosa Publishing House. Arumugam, S. , Joseph, J. P. 1999 On graphs with equal domination and connected domination numbers, Discrete Mathematics vol. 206, 45-49. Deo, N. 2005 Graph Theory with Applications to Engineering and Computer Science, Prentice-Hall of India Private Limited. Saoud, M. , Jebran, J. 2009 Finding A Minimum Dominating Set by Transforming Domi...