The Wiener number of a connected graph is equal to the sum of distances between all pairs of its vertices. A graph formed by a row of n hexagonal cells is called an n-hexagonal chain. Wiener number of an n x m hexagonal rectangle was found by the authors. An n x m hexagonal jagged-rectangle whose shape forms a rectangle and the number of hexagonal cells in each chain alternate between n and n 1...

In this note, we study the degree distance of a graph which is a degree analogue of the Wiener index. Given n and e, we determine the minimum degree distance of a connected graph of order n and size e.

The general Randić index Rα(G) is the sum of the weights (dG(u)dG(v)) over all edges uv of a (molecular) graph G, where α is a real number and dG(u) is the degree of the vertex u of G. In this paper, for any real number α ≤ −1, the minimum general Randić index Rα(T ) among all the conjugated trees (trees with a Kekulé structure) is determined and the corresponding extremal conjugated trees are ...

Let G be a connected graph, nu(e) is the number of vertices of G lying closer to u and nv(e) is the number of vertices of G lying closer to v. Then the Szeged index of G is defined as the sum of nu(e)nv(e), over edges of G.. The PI index of G is a Szeged-like topological index defined as the sum of [mu(e)+ mv(e)], where mu(e) is the number of edges of G lying closer to u than to v, mv(e) is the...