We study the number P(G) of non-equivalent ways of coloring a given graph G. We show some similarities and differences between this graph invariant and the well known chromatic polynomial. Relations with Stirling numbers of the second kind and with Bell numbers are also given. We then determine the value of this invariant for some classes of graphs. We finally study upper and lower bounds on P(...

We construct a one-parameter family of properly embedded minimal annuli in the Heisenberg group Nil3 endowed with a left-invariant Riemannian metric. These annuli are not rotationally invariant. This family gives a vertical half-space theorem and proves that each complete minimal graph in Nil3 is entire. Also, the sister surface of an entire minimal graph in Nil3 is an entire constant mean curv...

In this note, we introduce a graph invariant called the annihilation number and show that it is a sharp upper bound on the independence number. While the invariant does not distinguish between different graphs with the same degree sequence – since it is determined solely by the degrees – it still outperforms many well known upper bounds on independence number. The process which leads to the ann...

Two vertices of a graph are said to be similar if there exists a graph automorphism mapping one of them into the other. Procedures aiming to separate vertices of a graph into equivalence classes accordingly to their similarities are the basis of many isomorphism-testing algorithms. In practice, these procedures efficiently reduce the search space of backtracking-based techniques. We present a n...

* Institut de Physique du Globe, UMR 7516 ULP/CNRS, 5 rue Descartes, F-67084 Strasbourg Cedex, [email protected] ** Faculty of Geosciences, UCEL, University of Utrecht, P.O. Box 80115, 3508 TC Utrecht, The Netherlands *** CNR-IDPA, Sezione de Milano, Piazza della Scienza 1, I-20126 Milano, Italy. **** Geosyscom, Géographie des Systèmes de Communication, FRE 2795 CNRS, Univ...

I present a short review of the present status of the Standard Model prediction of the anomalous magnetic moment of the muon, with special emphasis on the hadronic contributions.

Hefftner, White, Alpert, and others observed a connection between topology and certain block designs with parameters k = 3 and ,I= 2. In this paper the connection is extended to include all values of I.. The topology is also exploited further to produce some new invariants of designs. The topology also gives an upper bound for the order of the automorphism group of the designs studied which lea...

This paper is comprised of two related parts. First we discuss which k-graph algebras have faithful traces. We characterise the existence of a faithful semifinite lowersemicontinuous gauge-invariant trace on C∗(Λ) in terms of the existence of a faithful graph trace on Λ. Second, for k-graphs with faithful gauge invariant trace, we construct a smooth (k,∞)summable semifinite spectral triple. We ...

The study examines whether the contrarian investment strategy, implies simultaneously buying previous losers and selling previous winners, exists in stock market of Taiwan. This study utilizes De Bondt and Thaler (1985) contrarian strategies into listed electronic and informational stocks in Taiwan from January of 1996 to December of 2004. The empirical results consistent with the findings of D...