## Abstract A (__p, q__)βgraph __G__ is said to be (__k, d__)βarithmetic if its vertices can be assigned distinct nonnegative integers so that the values of the edges, obtained as the sums of the numbers assigned to their end vertices, can be arranged in the arithmetic progression __k, k__ + __d, k
β¦ LIBER β¦
Geometry of arithmetic graphs
β Scribed by Yu. G. Grigor'yan
- Publisher
- Springer US
- Year
- 1983
- Tongue
- English
- Weight
- 504 KB
- Volume
- 18
- Category
- Article
- ISSN
- 1573-8337
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We study the graph X(n) that is de"ned as the "nite part of the quotient (n)!T, with T the Bruhat}Tits tree over % O ((1/ΒΉ )) and (n) the principal congruence subgroup of "GΒΈ(% We give concrete realizations of the ΒΈ-functions of the "nite part of the hal#ine !T for "nite unitary representations of