Infinite graphs with the least limiting eigenvalue greater than -2 (Q1087558)

The author proved previously that an infinite graph with -2\(\leq\) the least limiting eigenvalue (infimum of least eigenvalues of finite induced graphs) is a generalized line graph [On infinite graphs whose spectrum is greater than -2, Bull., Cl. Sci. Math. Nat., Sci. Math. 13, 21-35 (1984; Zbl 0548.05042)]. In this paper he characterizes graphs for which inequality is strict. The technique of proof is to divide the possibilities into cases and relate each case to an infinite family of finite graphs whose least eigenvalue can be analyzed. There is an error in the proof of Lemma 1: in Equation (*), n should be deleted. The least eigenvalue for each member of the family is then given by this equation (if \(n>1)\) and is independent of n; no consideration of limiting behavior is necessary. The proof of Prop. 6 is too brief.