1Department of Anesthesiology and Intensive Care Medicine, Northern State Medical University, Troitsky Avenue 51, Arkhangelsk 163000, Russia 2Department of Anesthesiology, University Hospital of North Norway, Tromsø, Norway 3Anesthesia and Critical Care Research Group, Department of Clinical Medicine, Faculty of Health Sciences, University of Tromsø, 9037 Tromsø, Norway 4Department of Anaesthes...

Enrico Carlon,* Péter Lajkó, Heiko Rieger, and Ferenc Iglói Theoretische Physik, Universität des Saarlandes, D-66041 Saarbrücken, Germany Department of Physics, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait Institute of Theoretical Physics, Szeged University, H-6720 Szeged, Hungary Research Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary ~Received 6 J...

-The Szeged index Sz is a recently introduced graph invariant, having applications in chemistry. In this paper, a formula for the Szeged index of Cartesian product graphs is obtained and some other composite graphs are considered. We also prove that for all connected graphs, Sz is greater than or equal to the sum of distances between all vertices. A conjecture concerning the maximum value of Sz...

Bertrand Berche†, Pierre Emmanuel Berche†‡, Ferenc Iglói§‖ and Gábor Palágyi¶ † Laboratoire de Physique des Matériaux , Université Henri Poincaré, Nancy 1 B.P. 239, F-54506 Vandœuvre les Nancy, France ‡ Institut für Physik, Johannes Gutenberg-Universität, Mainz Staudinger Weg 7, 55099 Mainz, Germany § Research Institute for Solid State Physics, H-1525 Budapest, P.O.Box 49, Hungary ‖ Institute f...

Department of Climatology and Landscape Ecology, University of Szeged, P.O.B. 653, 6701, Szeged, Hungary Department of Mechanical Engineering, Informatics Systems & Applications Group, Aristotle University, P.O. Box 483, 54124 Thessaloniki, Greece Department of Meteorology, Eötvös Loránd University, Pázmány Péter st. 1/A, 1117 Budapest, Hungary Mathematical Institute of the Hungarian Academy of...

The revised edge-Szeged index of a connected graph $G$ is defined as Sze*(G)=∑e=uv∊E(G)( (mu(e|G)+(m0(e|G)/2)(mv(e|G)+(m0(e|G)/2) ), where mu(e|G), mv(e|G) and m0(e|G) are, respectively, the number of edges of G lying closer to vertex u than to vertex v, the number of ed...

Let Sz(G), Sz(G) and W (G) be the Szeged index, revised Szeged index and Wiener index of a graph G. In this paper, the graphs with the fourth, fifth, sixth and seventh largest Wiener indices among all unicyclic graphs of order n > 10 are characterized; and the graphs with the first, second, third, and fourth largest Wiener indices among all bicyclic graphs are identified. Based on these results...

Let W (G) and Sz(G) be the Wiener index and the Szeged index of a connected graph G. It is proved that if G is a connected bipartite graph of order n ≥ 4, size m ≥ n, and if ` is the length of a longest isometric cycle of G, then Sz(G) − W (G) ≥ n(m − n + ` − 2) + (`/2) − ` + 2`. It is also proved if G is a connected graph of order n ≥ 5 and girth g ≥ 5, then Sz(G) − W (G) ≥ PIv(G) − n(n − 1) +...

let $g$ be a non-abelian group and let $z(g)$ be the center of $g$. associate with $g$ there is agraph $gamma_g$ as follows: take $gsetminus z(g)$ as vertices of$gamma_g$ and joint two distinct vertices $x$ and $y$ whenever$yxneq yx$. $gamma_g$ is called the non-commuting graph of $g$. in recent years many interesting works have been done in non-commutative graph of groups. computing the clique...