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\centerline{\bf \Large Errata}

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Besides small typos (missing points, commas or similar), so far I
realized the following:

\begin{enumerate}
\item p.\, 7, definition of a double nested graph: The first
sentence in the definition should be removed.

\item p.\, 9, Eqs. (1.2) and (1.3): Instead of $A$, there should
be $M$.


\item p.\, 11, text below (1.6): Instead of `$\lambda\leq
\Delta$', there should be `$|\lambda|\leq \Delta$'.

\item p. 28, last but one paragraph; p.\, 256 paragraph 1; refs
[22, 95, 172, 295]: Instead of `Lov\' as', there should be `Lov\'
asz'. (I apologize to Professor L\' aszl\' o Lov\' asz.)

\item p. 34, Eq. (2.14): Instead of $2m$, there should be $m$.

\item p.\, 58, line 1; p.\, 113, paragraph below Theorem 4.13:
Instead of `Friedland', there should be `Friedman'; p.\, 272, ref.
[164]: Instead of `Friedland, S.', there should be `Friedman, J.'.
(I apologize to Professor Joel Friedman.)

\item p.\, 88, Theorem 3.1: Remove `spanning'.

\item p.\, 92, proof of Theorem 3.12: Instead of $\widehat{H}$,
there should be $\widehat{G}$. Instead of $G$, there should be
$H$.

\item p. 110, Theorem 4.8: the partition mentioned in the proof is
not equitable (as I said), but this fact does not affect the
proof.

\item p. 111, Theorem 4.10: Instead of `Tanner et al.', there
should be `Cheeger'.

\item p. 129, Theorem 4.38: The graph $K_{4,4}$ is missing.

\item p.\, 133, Remark 4.46: In the 1st paragraph, instead of `...
determined in [428] (there are 24 such graphs).', there should be
`... determined in [428], see an erratum in [Stevanovi\' c, D., de
Abreu, N.\,M.\,M., de Freitas, M.\,A.\,A., Del-Vecchio, R. Walks
and regular integral graphs. {\em Linear Algebra Appl.},
\textbf{423} (2007), 119--135.] (there are 25 such graphs).' In
the 2nd paragraph, instead of `... the Cartesian product...',
there should be `... the tensor product...'. In the 2nd paragraph,
instead of `... exactly 16 resulting...', there should be `...
exactly 17 resulting...'. Mentioned reference should be added to
the list.

\item p.\, 149, paragraph 2: Instead of `Bearing in mind that any
DNG is a bipartite graph which does not contain any of the graphs
$P_4,C_4$ or $2K_2$ as an induced subgraph, we easily verify the
following fact.', there should be `We easily verify the following
fact.'

\item p.\, 156, Eq. (6.4): Instead of $\mu_1$ on the left hand
side, there should be $\mu_1^2$.

\end{enumerate}



If you notice something similar, please let me know!

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Last modified \today.



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