The corona product G ◦ H of two graphs G and H is obtained by taking one copy of G and |V (G)| copies of H; and by joining each vertex of the i-th copy of H to the i-th vertex of G, where 1 ≤ i ≤ |V (G)|. In this paper, exact formulas for the eccentric distance sum and the edge revised Szeged indices of the corona product of graphs are presented. We also study the conditions under which the cor...

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.

The second and third geometric-arithmetic indices GA2(G) and GA3(G) of a graph G are defined, respectively, as ∑ uv∈E(G) √ nu(e,G)nv(e,G) 1 2 [nu(e,G)+nv(e,G)] and ∑ uv∈E(G) √ mu(e,G)mv(e,G) 1 2 [mu(e,G)+mv(e,G)] , where e = uv is one edge in G, nu(e,G) denotes the number of vertices in G lying closer to u than to v andmu(e,G) denotes the number of edges in G lying closer to u than to v. The Sz...

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...