A. Abdollahi and A. Loghman On one-factorizations of replacement
products. to appear in {\em Filomat}, Published by Faculty of
Sciences and Mathematics, University of Ni\v{s}, Serbia, available
at \href{http://www.pmf.ni.ac.rs/filomat}{http://www.pmf.ni.ac.rs/filomat}. N. Alon (1986). Eigenvalues and expanders. Combinatorica. 6 (2), 83-96 N. Alon, A. Lubotzky and A. Wigderson (2001). Semi-direct product in groups and zig-zag product in graphs. connections and applications (extended abstract), in:
{\em \lq\lq $42$-nd IEEE Symposium on Foundations of Computer
Science, Las Vegas, NV, 2001\rq\rq}, {\em IEEE Computer
Soc.}, Los Alamitos, CA. , 630-637 N. Alon and V. D. Milman (1985). $\lambda_1$,
isoperimetric inequalities for graphs, and superconcentrators. J. Combin. Theory Ser. B. 38 (1), 73-88 T. Austin, A. Naor and A. Valette (2010). The Euclidean
Distortion of the Lamplighter Group. Discrete Comput. Geom.. 44 (1), 55-74 L. Bartholdi and W. Woess (2005). Spectral
computations on lamplighter groups and Diestel-Leader graphs. 11 (2), 175-202 T. Ceccherini-Silberstein, F. Scarabotti and F.
Tolli (2008). Harmonic Analysis on Finite Groups. Representation theory. Gelfand pairs and Markov chains, {em Cambridge Studies in
Advanced Mathematics}, Cambridge University Press, Cambridge,
xiv + 440 pp.. 180 J. J. Cummings and C. A. Kelley On the Independence and Domination Numbers
of Replacement Product Graphs. submitted, available at
href{http://www.math.ucsd.edu/$sim$jjcummings/RP$_{-}$Submission$_{-}$Final.pdf}
{http://www.math.ucsd.edu/$sim$jjcummings/RP$_{-}$Submission$_{-}$Final.pdf}. D. D'Angeli and A. Donno (2009). Crested products of Markov chains. Ann. Appl. Probab.. 19 (1), 414-453 D. D'Angeli and A. Donno (2010). Markov chains on orthogonal block structures. European J. Combin.. 31 (1), 34-46 D. D'Angeli and A. Donno (2011). Generalized crested products of Markov chains. European J. Combin.. 32 (2), 243-257 G. Davidoff, P. Sarnak and A. Valette (2003). Elementary number theory, group theory, and Ramanujan graphs. London Mathematical Society Student Texts, Cambridge University Press, Cambridge, x + 144 pp.. 55 E. Dobson and J. Morris (2009). Automorphism Groups of Wreath Product
Digraphs. Electron. J. Combin., RP 17.. 16 (1) J. Dodziuk (1984). Difference equations, isoperimetric
inequality and transience of certain random walks. Trans.
Amer. Math. Soc.. 284 (2), 787-794 A. Donno Generalized wreath products of graphs
and groups. submitted. A. Erschler (2006). Generalized wreath products. IMRN Int. Math. Res. Notices, Article ID 57835. , 1-14 R. I. Grigorchuk and A. .{Z}uk (2001). The
lamplighter group as a group generated by a $2$-state automaton, and its spectrum. Geom. Dedicata. 87 (1-3), 209-244 M. Gromov (1983). Filling Riemannian manifolds. J. Differential
Geom.. 18 (1), 1-147 R. Hammack, W. Imrich and S. Klav\v{z}ar (2011). Handbook of product graphs. Second edition. Discrete Mathematics and its Applications (Boca Raton)}. CRC
Press, Boca Raton, FL, xviii + 518 pp.. F. Harary (1959). On the group of the composition of two
graphs. Duke Math. J.. 26, 29-34 S. Hoory, N. Linial and A. Wigderson (2006). Expander
graphs and their applications. Bull. Amer. Math. Soc. (N.S.). 43 (4), 439-561 W. Imrich and H. Izbicki (1975). Associative Products of
Graphs. Monatsh. Math.. 80 (4), 277-281 C. A. Kelley, D. Sridhara and J. Rosenthal (2008). Zig-zag and replacement product graphs and LDPC codes. Adv. Math.
Commun.. 2 (4), 347-372 A. Lubotzky (2012). Expander graphs in pure and
applied mathematics. Bull. Amer. Math. Soc. (N.S.). 49 (1), 113-162 A. Lubotzky and B. Weiss (1993). Groups and expanders. Expanding
graphs (Princeton, NJ, 1992), DIMACS Ser. Discrete
Math. Theoret. Comput. Sci., Amer. Math. Soc.,
Providence, RI. 10, 95-109 G. A. Margulis (1973). Explicit constructions of
expanders. Problemy Pereda\v{c}i Informacii, Russian. 9 (4), 71-80 Y. Peres and D. Revelle (2004). Mixing times for random walks on finite lamplighter groups. Electron. J. Probab.. 9 (26), 825-845 M. S. Pinsker (June 1973). On the complexity of a concentrator. $7$th International Teletraffic Conference, Stockolm, pages 318/1-318/4. , 1-4 O. Reingold, S. Vadhan and A. Wigderson (2002). Entropy
Waves, the Zig-Zag Graph Product, and New Constant-Degree
Expanders. Ann. of Math. (2). 155 (1), 157-187 G. Sabidussi (1959). The composition of graphs. Duke Math.
J.. 26, 693-696 G. Sabidussi (1959/1960). Graph multiplication. Math.
Z.. 72, 446-457 F. Scarabotti and F. Tolli (2009). Radon transforms and lamplighter random walks. J. Math. Sci. (N.Y.), translated from Sovrem. Mat. Prilozh. (Contemporary
Mathematics and Its Applications), Vol. 50, Functional Analysis,
2007.. 156 (1), 109-122 F. Scarabotti and F. Tolli (2008). Harmonic
Analysis on finite lamplighter random walks. J. Dyn. Control
Syst.. 14 (2), 251-282 F. Scarabotti and F. Tolli (2010). Harmonic analysis on a finite
homogeneous space. Proc. Lond. Math. Soc. (3). 100 (2), 348-376 W. Woess (2005). A note on the norms of transition
operators on lamplighter graphs and groups. Internat. J.
Algebra Comput.. 15 (5-6), 1261-1272