Estrada, Ernesto (2012) The communicability distance in graphs. Linear Algebra and Its Applications, 436 (11). pp. 4317-4328. ISSN 0024-3795Full text not available in this repository. (Request a copy from the Strathclyde author)
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.
|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:||07 Jan 2017 01:20|