Isomorphism types of some infinite graphs

Author: Archil Kipiani
Keywords: infinite graphs, isomorphism types, automorphisms group
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On isomorphism types of some infinite graphs In the papers [6] and [7], for any ordinal number α, we have constructed a root tree with verteces set ωα , which has the trivial automorphisms group. Now we consider some graphs that are built with the aid of this tree, and some of their applications to combinatorial problems considered in [1]-[5]. This research was supported by Rustaveli NSF Grant: GNSF/ST 09_144_3-105 R e f e r e n c e s [1] C.M. Bang, Isomorphism types of infinite symmetric graphs, Proceedings of the American Mathematical Society, v. 35. no. 1, 1972, pp. 31-33. [2] S.D. Comer and J.J. Le Tourneau, Isomorphism types of infinite algebras, Proceedings of the American Mathematical Society, v. 21, no. 3, 1969, pp. 635-639. [3] B. Jonsson, Topics in universal algebra, Springer-Verlag, Berlin, 1972. [4] G. Sabidussi, Graphs with given infinite group, Monatshefte für Mathematik, v. 64, no.1, 1960, pp. 64–67. [5] S. Ulam, A Collection of Mathematical Problems, New York, Interscience Publishers, 1960. 6. Archil Kipiani, One abstract characterization of intervals of cardinal numbers, Acta Univ. Lodz. Folia Math., no. 9, 1997, pp. 55--61. 7. Archil Kipiani, Uniform sets and isomorphisms of trees. Preprint no 107, Mathematical Institute University of Wrociaw, 1989, 10 p.