The edge-Szeged index is recently introduced graph invariant, having applications in chemistry. In this paper, a method of calculating the edge-Szeged index of hexagonal chain is proposed, and the results of the index are presented.

hansen et‎. ‎al.‎, ‎using the autographix software ‎package‎, ‎conjectured that the szeged index $sz(g)$ and the‎ ‎wiener index $w(g)$ of a connected bipartite graph $g$ with $n geq ‎4$ vertices and $m geq n$ edges‎, ‎obeys the relation‎ ‎$sz(g)-w(g) geq 4n-8$‎. ‎moreover‎, ‎this bound would be the best possible‎. ‎this paper offers a proof to this conjecture‎.

topological indices are numerical parameters of a graph which characterize its topology. inthis paper the pi, szeged and zagreb group indices of the tetrameric 1,3–adamantane arecomputed.

We study distance-based graph invariants, such as the Wiener index, the Szeged index, and variants of these two. Relations between the various indices for trees are provided as well as formulas for line graphs and product graphs. This allows us, for instance, to establish formulas for the edge Wiener index of Hamming graphs, C4nanotubes and C4-nanotori. We also determine minimum and maximum of ...

János Kokavecz,1,* Othmar Marti,2 Péter Heszler,3,4 and Ádám Mechler5,† 1Department of Optics and Quantum Electronics, University of Szeged, P.O. Box 406, H-6701 Szeged, Hungary 2Department of Experimental Physics, University of Ulm, Albert-Einstein-Allee 11 D-89069 Ulm, Germany 3Research Group on Laser Physics of the Hungarian Academy of Sciences, P.O. Box 406, H-6701 Szeged, Hungary 4The Ångs...

The weighted Szeged index of a connected graph G is defined as Szw(G) = ∑ e=uv∈E(G) ( dG(u) + dG(v) ) nu (e)n G v (e), where n G u (e) is the number of vertices of G whose distance to the vertex u is less than the distance to the vertex v in G. In this paper, we have obtained the weighted Szeged index Szw(G) of the splice graph S(G1, G2, y, z) and link graph L(G1, G2, y, z).

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...

Let (G,w) be a network, that is, a graph G = (V (G), E(G)) together with the weight function w : E(G) → R. The Szeged index Sz(G,w) of the network (G,w) is introduced and proved that Sz(G,w) ≥ W (G,w) holds for any connected network where W (G,w) is the Wiener index of (G,w). Moreover, equality holds if and only if (G,w) is a block network in which w is constant on each of its blocks. Analogous...

Recently, it was conjectured by Gutman and Ashrafi that the complete graph Kn has the greatest edge-Szeged index among simple graphs with n vertices. This conjecture turned out to be false, but led Vukičević to conjecture the coefficient 1/15552 of n6 for the approximate value of the greatest edge-Szeged index. We provide counterexamples to this conjecture.