the edge versions of reverse wiener indices were introduced by mahmiani et al. veryrecently. in this paper, we find their relation with ordinary (vertex) wiener index in somegraphs. also, we compute them for trees and tuc4c8(s) naotubes.

The Wiener index W(G) of a connected graph G is defined as the sum of the distances between all unordered pairs of vertices of G. The eccentricity of a vertex v in G is the distance to a vertex farthest from v. In this paper we obtain the Wiener index of a graph in terms of eccentricities. Further we extend these results to the self-centered graphs.

let g be a graph. the first zagreb m1(g) of graph g is defined as: m1(g) = uv(g) deg(u)2. in this paper, we prove that each even number except 4 and 8 is a first zagreb index of a caterpillar. also, we show that the fist zagreb index cannot be an odd number. moreover, we obtain the fist zagreb index of some graph operations.

Let G = (V, E) be a simple graph. Hosoya polynomial of G is d(u,v) H(G, x) = {u,v}V(G)x , where, d(u ,v) denotes the distance between vertices u and v. As is the case with other graph polynomials, such as chromatic, independence and domination polynomial, it is natural to study the roots of Hosoya polynomial of a graph. In this paper we study the roots of Hosoya polynomials of some specific g...

In this paper, we prove the existence of fixed point for Chatterjea type mappings under $c$-distance in cone metric spaces endowed with a graph. The main results extend, generalized and unified some fixed point theorems on $c$-distance in metric and cone metric spaces.