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 â‰¥ 4, size m â‰¥ n, and if ` is the length of aâ€¦ (More)

The vertex PI index of a graph G is the sum over all edges uv âˆˆ E(G) of the number of vertices which are not equidistant to u and v. In this paper, the extremal values of this new topological indexâ€¦ (More)

Let (G,w) be a network, that is, a graph G = (V (G), E(G)) together with the weight function w : E(G) â†’ R. The Szeged index Sz(G,w) of the network (G,w) is introduced and proved that Sz(G,w) â‰¥ Wâ€¦ (More)

Let Sz(G) and W (G) be the revised Szeged index and the Wiener index of a graph G. Chen, Li, and Liu [European J. Combin. 36 (2014) 237â€“246] proved that if G is a non-bipartite connected graph ofâ€¦ (More)

The power graph P(G) of a group G is the graph whose vertex set is the group elements and two elements are adjacent if one is a power of the other. In this paper, we consider some graph theoreticalâ€¦ (More)

Average distance is an important parameter for measuring the communication cost of computer networks. A popular approach for its computation is to first partition the edge set of a network intoâ€¦ (More)

Let G be a connected graph of order n. The long-standing open and close problems in distance graph theory are: what is the Wiener index W (G) or average distance Î¼(G) among all graphs of order n withâ€¦ (More)

Let G be a connected graph and Î¾(G) = Sze(G)âˆ’We(G), where We(G) denotes the edge Wiener index and Sze(G) denotes the edge Szeged index of G. In an earlier paper, it is proved that if T is a tree thenâ€¦ (More)