Abstract: This paper develops properties of the adjacency-type sequences defined from the adjacency matrix of the Cayley diagram for the direct product of two cyclic groups of order n and m. Also, we study the adjacency-type sequences modulo a from the generating matrices of the adjacency-type sequences when read modulo a. Then we derive the relationships among the orders of the obtained cyclic groups and the periods of the adjacency-type sequences modulo a. Furthermore, we extend the adjacency-type sequences to groups and then we obtain the period of the adjacency-type sequence in the quaternion group Q8.
Key words: The Adjacency-Type Sequences; Group; Matrix; Period.
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How to cite this article:
Omur Deveci and Anthony G. Shannon, On The Adjacency-Type Sequences, International Journal of Advances in Mathematics, Volume 2017, Number 2, Pages 10-24, 2017.