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 (https://doi.org/10.1016/j.laa.2012.01.017)
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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.
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Item type: Article ID code: 40664 Dates: DateEvent1 June 2012PublishedSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 02 Aug 2012 10:53 Last modified: 21 Jan 2024 05:48 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/40664