# The communicability distance in graphs

Estrada, Ernesto
(2012)
*The communicability distance in graphs.*
Linear Algebra and Its Applications, 436 (11).
pp. 4317-4328.
ISSN 0024-3795

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 |
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ID code: | 40664 |

Keywords: | matrix functions, Euclidean distance, graph spectrum, graph distance, communicability, Mathematics, Discrete Mathematics and Combinatorics, Algebra and Number Theory, Geometry and Topology, Numerical Analysis |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics |

Depositing user: | Pure Administrator |

Date Deposited: | 02 Aug 2012 10:53 |

Last modified: | 09 Dec 2016 10:30 |

Related URLs: | |

URI: | http://strathprints.strath.ac.uk/id/eprint/40664 |

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