60/102 Null Boundary Cellular Automata based expander graphs

Abstract : Expander graphs are useful in the design and analysis of communication networks. Mukhopadhyay et al. introduced a method to generate a family of expander graphs based on nongroup two predecessor single attractor Cellular Automata(CA). In this paper we propose a method to generate a family of expander graphs based on 60/102 Null Boundary CA(NBCA) which is a group CA. The spectral gap generated by our method is maximal. Moreover, the spectral gap is larger than that of Mukhopadhyay et al.
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Fatès, Nazim and Kari, Jarkko and Worsch, Thomas. Automata 2010 - 16th Intl. Workshop on CA and DCS, 2010, Nancy, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AL, Automata 2010 - 16th Intl. Workshop on CA and DCS, pp.19-28, 2010, DMTCS Proceedings
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Sung-Jin Cho, Un-Sook Choi, Han-Doo Kim, Yoon-Hee Hwang, Jin-Gyoung Kim. 60/102 Null Boundary Cellular Automata based expander graphs. Fatès, Nazim and Kari, Jarkko and Worsch, Thomas. Automata 2010 - 16th Intl. Workshop on CA and DCS, 2010, Nancy, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AL, Automata 2010 - 16th Intl. Workshop on CA and DCS, pp.19-28, 2010, DMTCS Proceedings. 〈hal-01185496〉

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