| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 418995 | Discrete Applied Mathematics | 2015 | 7 Pages |
Abstract
The Harary index of a graph is defined as the sum of reciprocals of distances between all pairs of vertices of the graph. In this paper we provide an upper bound of the Harary index in terms of the vertex or edge connectivity of a graph. We characterize the unique graph with the maximum Harary index among all graphs with a given number of cut vertices or vertex connectivity or edge connectivity. In addition we also characterize the extremal graphs with the second maximum Harary index among all graphs with given vertex connectivity.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Xiao-Xin Li, Yi-Zheng Fan,