In this paper we propose and study a new structural invariant for graphs, called distance-
unbalancedness, as a measure of how much a graph is (un) balanced in terms of distances …

The Wiener index is defined as the sum of distances between all unordered pairs of vertices
in a graph. It is one of the most recognized and well-researched topological indices, which is …

The Wiener index of a connected graph is the sum of the distances between all unordered
pairs of vertices. A connected graph is Eulerian if its vertex degrees are all even. In Gutman …

Topological indices, ie, numerical invariants suitably associated to graphs and only
depending upon their isomorphism type, have important applications in Chemistry. Their …

The Wiener index (the distance) of a connected graph is the sum of distances between all
pairs of vertices. In this paper, we study the maximum possible value of this invariant among …

A strong orientation of a graph $ G $ is an assignment of a direction to each edge such that $
G $ is strongly connected. The oriented diameter of $ G $ is the smallest diameter among all …

In the recent literature there are numerous publications concerned with a graph invariant
named “Gutman index”(ZZ). In this paper, some details about the discovery of ZZ are …

For a graph G, let nG (u, v) be the number of vertices of G that are strictly closer to u than to v.
The distance–unbalancedness index uB (G) is defined as the sum of| nG (u, v)− nG (v, u) …