Estrada, Ernesto (2012) The communicability distance in graphs. Linear Algebra and Its Applications, 436 (11). pp. 4317-4328. ISSN 0024-3795
Full text not available in this repository. (Request a copy from the Strathclyde author)Official URL: http://dx.doi.org/10.1016/j.laa.2012.01.017
Abstract
Let G be a simple connected graph with adjacency matrix A. The communicabilityGpq between two nodes p and q of the graph is defined as the pq-entry of G=exp(A). We prove here that ξp,q=(Gpp+Gqq-2Gpq)1/2 is a Euclidean distance and give expressions for it in paths, cycles, stars and complete graphs with n nodes. The sum of all communicabilitydistances in a graph is introduced as a new graph invariant ϒ(G). We compare this index with the Wiener and Kirchhoff indices of graphs and conjecture about the graphs with maximum and minimum values of this index.
| Item type: | Article |
|---|---|
| ID code: | 40664 |
| Keywords: | matrix functions, Euclidean distance, graph spectrum, graph distance, communicability, Mathematics |
| Subjects: | Science > Mathematics |
| Department: | Faculty of Science > Mathematics and Statistics |
| Related URLs: | |
| Depositing user: | Pure Administrator |
| Date Deposited: | 02 Aug 2012 11:53 |
| Last modified: | 02 Aug 2012 11:53 |
| URI: | http://strathprints.strath.ac.uk/id/eprint/40664 |
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