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

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  •   Jangiti Devendra

  •   Levaku Madhavi

  •   Tippaluri Nagalakshumma

Abstract

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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How to Cite
Devendra, J., Madhavi, L., & Nagalakshumma, T. (2022). Enumeration of Triangles and Hamiltonian Property of The Zero-Divisor Cayley Graph of The Ring G(Zₙ,⊕,⊙). European Journal of Mathematics and Statistics, 3(4), 37–42. https://doi.org/10.24018/ejmath.2022.3.4.106