Abstract
This chapter discusses the graphs of type 1z that are Cayley graphs of groups Z(m,n,k), where n > 2. There are 10 such groups of order 2 mn ≤ 120. The chapter presents the numerical properties of these groups. The two values of k given for each group are inverses (mod m); therefore, they yield isomorphic Cayley graphs. The relation S2n = E implies the existence of (2n)gons in the Cayley graph; therefore, the girth g of the graph satisfies the inequality g ≤ 2n. The girth of the graph cannot be higher than 10, and from a diagram, it can be seen that it is indeed 10. The chapter also describes the Hamiltonian circuit with the non-antipalindromic LCF code.
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