István A. Kovács∗,1, 2, 3 Réka Mizsei, and Péter Csermely Wigner Research Centre, Institute for Solid State Physics and Optics, H-1525 Budapest, P.O.Box 49, Hungary Institute of Theoretical Physics, Szeged University, H-6720 Szeged, Hungary Center for Complex Networks Research and Department of Physics, Northeastern University, 110 Forsyth Street, 111 Dana Research Center, Boston, MA 02115, USA...

In the modern literature on game theory there are several versions of what is known as Zermelo’s theorem. It is shown that most of these modern statements of Zermelo’s theorem bear only a partial relationship to what Zermelo really did. We also give a short survey and discussion of the closely related but almost unknown work by König (1927, Acta Sci. Math. Szeged, 3, 121–130) and Kálmar (1928/2...

The edge Szeged index of a connected graph G is defined as the sum of products mu(e|G)mv(e|G) over all edges e = uv of G, where mu(e|G) is the number of edges whose distance to vertex u is smaller than the distance to vertex v, and mv(e|G) is the number of edges whose distance to vertex v is smaller than the distance to vertex u. In this paper, we determine the n-vertex unicyclic graphs with th...

Complete List of Authors: Oláh, Attila; University of Debrecen, Department of Physiology Ambrus, Lídia; University of Debrecen, Department of Physiology Nicolussi, Simon; University of Bern, Institute of Biochemistry and Molecular Medicine, NCCR TransCure Gertsch, Jürg; University of Bern, Institute of Biochemistry and Molecular Medicine, NCCR TransCure Tubak, Vilmos; Creative Laboratory Ltd, K...

The aim of the study is to define those factors, which are relevant in forming weather and air quality conditions in Szeged, Hungary. The database consists of daily averages of 11 meteorological and 8 air pollution parameters for the summer and winter months for the five-year period 1997-2001. In order to explain the connections between the 19 variables, the multivariate statistical method of f...

Szeged 2004 " Computers are good at following instructions, but not at reading your mind. " — Donald E. Knuth

Let e be an edge of a G connecting the vertices u and v. Define two sets N1 (e | G) and N2(e |G) as N1(e | G)= {xV(G) d(x,u) d(x,v)} and N2(e | G)= {xV(G) d(x,v) d(x,u) }.The number of elements of N1(e | G) and N2(e | G) are denoted by n1(e | G) and n2(e | G) , respectively. The Szeged index of the graph G is defined as Sz(G) ( ) ( ) 1 2 n e G n e G e E    . In this paper we compute th...

ABSTRACT Let ‎G=(V,E) ‎be a‎ ‎simple ‎connected ‎graph ‎with ‎vertex ‎set ‎V‎‎‎ ‎and ‎edge ‎set ‎‎‎E. ‎The Szeged index ‎of ‎‎G is defined by ‎ where ‎ respectively ‎ ‎ is the number of vertices of ‎G ‎closer to ‎u‎ (‎‎respectively v)‎ ‎‎than ‎‎‎v (‎‎respectively u‎).‎ ‎‎If ‎‎‎‎S ‎is a‎ ‎set ‎of ‎size‎ ‎ ‎ ‎let ‎‎V ‎be ‎the ‎set ‎of ‎all ‎subsets ‎of ‎‎S ‎of ‎size ‎3. ‎Then ‎we ‎define ‎t...

the edge szeged index is a new molecular structure descriptor equal to the sum of products mu(e)mv(e) over all edges e = uv of the molecular graph g, where mu(e) is the number of edges which its distance to vertex u is smaller than the distance to vertex v, and nv(e) is defined analogously. in this paper, the edge szeged index of one-pentagonal carbon nanocone cnc5[n] is computed for the first ...