Enumeration of Triangles and Hamiltonian Property of The Zero-Divisor Cayley Graph of The Ring G(Zₙ,⊕,⊙)



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Submitted Mar 6, 2022
Published Jul 28, 2022
10.24018/ejmath.2022.3.4.106

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In this paper an enumeration method to find the number of triangles in the zero-divisor Cayley graph G(Zₙ,D₀ ) associated with the ring (Zₙ,⨁,⨀),n≥1 of integers modulo n,  an integer and its subset D0 of zero-divisors is presented. Further it is shown that this graph is Hamiltonian, not bipartite  and  Eulerian graph when n is odd.

 

Keywords: Zero-divisor, Zero-divisor Cayley graph, Triangle, Basic triangle and Hamilton cycle

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