Can one hear the shape of permutation group?
Keywords:
Spectra of Graphs and Groups, Lie geometries, coherent configurations, distance-regular graphs, small world graphs, geometrical expandersAbstract
Missing definitions of the theory of permutation groups and algebraic graph theory such as coherent configuratuion, orbital of permutation group, distance regular and distance transitive graphs, extended bipartite double of graph reader can find in [1], [2] or [3].
References
Higman, D.G., Coherent Configurations. Part I. Ordinary Representation Theory, GeometriaeDedicata, 4 (1975), 1–32.
A. E. Brouwer, A. M. Cohen and A. Neumaier, Distance-regular Graphs, Springer-Verlag, Berlin, 1989.
Peter. J. Cameron, Coherent configurations, association schemes and permutation groups, Groups, Combinatorics and Geometry,2003, pp. 55-71.
I. A. Faradzev, M. H. Klin, M. E. Muzichuk, Cellular Rings and Groups of Automorphisms of Graphs, Investigations in Algebraic Theory of Combinatorial Objects, Kluwer, Dordrecht (1992). pp.1-152.
M. Cvetkovic, M. Doob, I. Gootman, A. Targasev, Theory of Graph Spectra, Ann.Disc. Math., 36 (1988), North Holland.
N. Alon, Eigenvalues, geometric expanders, sorting in rounds, and ramsey theory, Combinatirica, 1986, Volume 6, issue 3, pp 207–219.
V. Ustimenko, On some properties of the geometries of Chevalley groups and their generalizations, Investigations in Algebraic Theory of Combinatorial Objects, Kluwer, Dordrecht (1992). p. 112-119. (Translation from Proceeding of VNIISI, Moscow, 1978 (in Russian).
J. Hemmeter, Distance-Regular Graphs and Halved Graphs , J. Combina- torics (1986) 7, 119-129.
Edwin R. van Dam, Jack H. Koolen, Hajime Tanaka, Distance Regular Graphs, The Electronic Journal of Combinatorics, Dynamic Survey, DS22, 2016.
A. Brouwer, D. Pasechnik, Two distance-regular graphs, J. Algebraic Combin., 36 (2012).
V. Ustimenko, On small world Non-Sunada twins and cellular Voronoi diagrams, Algebra and Discrete Math (to appear).
M. Erwig, The graph Voronoi diagram with applications, Networks, vol. 36 (2000), no. 3, pp. 156-163.
