منابع مشابه
The Szeged and the Wiener Index of Graphs
-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...
متن کاملImproved bounds on the difference between the Szeged index and the Wiener index of graphs
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) +...
متن کاملThe quotients between the (revised) Szeged index and Wiener index of graphs
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...
متن کاملOn the revised edge-Szeged index of graphs
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...
متن کاملWiener index versus Szeged index in networks
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...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 1996
ISSN: 0893-9659
DOI: 10.1016/0893-9659(96)00071-7