scholarly journals The algebra of metric betweenness II: Geometry and equational characterization of weakly median graphs

2008 ◽  
Vol 29 (3) ◽  
pp. 676-700 ◽  
Author(s):  
Hans-Jürgen Bandelt ◽  
Victor Chepoi
Keyword(s):  
Median Graphs ◽  
Equational Characterization

scholarly journals AXIOMATIC CHARACTERIZATION OF THE ANTIMEDIAN FUNCTION ON PATHS AND HYPERCUBES

2012 ◽  
Vol 04 (04) ◽  
pp. 1250054 ◽  
Author(s):  
KANNAN BALAKRISHNAN ◽  
MANOJ CHANGAT ◽  
HENRY MARTYN MULDER ◽  
AJITHA R. SUBHAMATHI
Keyword(s):  
Axiomatic Characterization ◽  
Median Graphs ◽  
Obnoxious Facility ◽  
Location Function ◽  
Median Function

An antimedian of a profile π = (x1, x2, …, xk) of vertices of a graph G is a vertex maximizing the sum of the distances to the elements of the profile. The antimedian function is defined on the set of all profiles on G and has as output the set of antimedians of a profile. It is a typical location function for finding a location for an obnoxious facility. The 'converse' of the antimedian function is the median function, where the distance sum is minimized. The median function is well studied. For instance it has been characterized axiomatically by three simple axioms on median graphs. The median function behaves nicely on many classes of graphs. In contrast the antimedian function does not have a nice behavior on most classes. So a nice axiomatic characterization may not be expected. In this paper such a characterization is obtained for two classes of graphs on which the antimedian is well behaved: paths and hypercubes.

scholarly journals The Powerdomain of Indexed Valuations

2002 ◽  
Vol 9 (38) ◽  
Author(s):  
Daniele Varacca
Keyword(s):  
Denotational Semantics ◽  
Point Of View ◽  
Domain Theory ◽  
Theoretic Point ◽  
Equational Characterization ◽  
Imperative Language

This paper is about combining nondeterminism and probabilities. We study this phenomenon from a domain theoretic point of view. In domain theory, nondeterminism is modeled using the notion of powerdomain, while probability is modeled using the powerdomain of valuations. Those two functors do not combine well, as they are. We define the notion of powerdomain of indexed valuations, which can be combined nicely with the usual nondeterministic powerdomain. We show an equational characterization of our construction. Finally we discuss the computational meaning of indexed valuations, and we show how they can be used, by giving a denotational semantics of a simple imperative language.

scholarly journals Equational Characterization of All Varieties of MV-Algebras

1999 ◽  
Vol 221 (2) ◽  
pp. 463-474 ◽  
Author(s):  
Antonio Di Nola ◽  
Ada Lettieri
Keyword(s):  
Equational Characterization ◽  
Mv Algebras

scholarly journals A new characterization of median graphs

1994 ◽  
Vol 128 (1-3) ◽  
pp. 385-387 ◽  
Author(s):  
Abdelhafid Berrachedi
Keyword(s):  
Median Graphs
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