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Some relations between graph theory and Riemann surfaces. (English) Zbl 0890.30027
Zalcman, Lawrence (ed.), Proceedings of the Ashkelon workshop on complex function theory, Ashkelon, Israel, May 13–16, 1996. Ramat-Gan: Bar-Ilan University, Isr. Math. Conf. Proc. 11, 61-73 (1997).
This paper gives a survey of various relationships between the theory of Riemann surfaces and graph theory. The problem which the author puts at the centre of his discussion is that whether isospectral objects are isometric. The most general construction of isospectral but nonisometric objects was given by T. Sunada. One can therefore ask whether this construction is the most general; the author gives an eample (due to himself and A. Lubotsky) of a putative example of two isospectral graphs which are not isometric and which cannot be obtained by the Sunada construction. The author also discusses several other related questions and poses a number of questions.
For the entire collection see [Zbl 0878.00056].

30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)
31C20 Discrete potential theory