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.
Highlights
Expander graphs were first defined by Bassalygo and Pinsker and their existence first proved by Pinsker in the early 1970s [10]
C be the n-cell 60/102 NBCA whose state transition matrix T is as the following:
Our results show that the spectral gap and the expansion increases proportionately with the number of union operations (t)
Summary
Expander graphs were first defined by Bassalygo and Pinsker and their existence first proved by Pinsker in the early 1970s [10]. 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. The merit of our method is that it use regular, modular and cascadable structure of 60/102 NBCA [1, 3, 4] to generate regular graphs of good expansion property with less storage. The spectral gap generated by our method is maximal. Kim [12] can be viewed as a discrete lattice of sites (cells), where each cell can assume the value either 0 or 1. If the next-state function of a cell is expressed in the form of a truth table, the decimal equivalent of the output is conventionally called the rule number for the cell
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