Remarks on Distance Distributions for Graphs Modeling Computer Networks |
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| Institution: | 1. Hochschule für Technik und Wirtschaft Berlin, Wilhelminenhofstraße 75A, D12459 Berlin, Germany;2. Faculty of Mathematics and Physics, University of Ljubljana, Jadranska ulica 21, 1000 Ljubljana, Slovenia;3. Institute of Mathematics, Physics and Mechanics, Jadranska ulica 19, 1000 Ljubljana, Slovenia;4. Faculty of Information Studies, Ljubljanska cesta 31A, p.p. 603, 8000 Novo mesto, Slovenia;5. Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska, GlagoljaÅ¡ka 8, 6000 Koper, Slovenia;1. Faculty of Mathematics and Statistics, Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, PR China;2. Faculty of Mathematics and Physics, Hubei Institute of Technology, Huangshi 435003, PR China |
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| Abstract: | The Wiener polynomial of a graph G is a generating function for the distance distribution dd(G) = (D1, D2,…,Dt), where Di is the number of unordered pairs of distinct vertices at distance i from one another and t is the diameter of G. We use the Wiener polynomial and several related generating functions to obtain generating functions for distance distributions of graphs that model certain large classes of computer networks. These provide a straightforward means of computing distance and timing statistics when designing new networks or enlarging existing networks. |
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