Abstract

Nilpotent Cayley Graph of the Residue Class Ring ( 𝒁𝒏,⊕, ⊙)

Tippaluri Nagalakshumma1, Jangiti Devendra2 and Levaku Madhavi3*

1Research Scholar, Department of Applied Mathematics, Yogi Vemana University, Kadapa-516005, A.P., INDIA. 2Research Scholar, Department of Applied Mathematics, Yogi Vemana University, Kadapa-516005, A.P., INDIA. 3*Assistant Professor, Department of Applied Mathematics, Yogi Vemana University, Kadapa-516005, A.P., INDIA.

ABSTRACT

In this paper the notion of the nilpotent Cayley graph 𝐺(𝑍𝑛,𝑁), where ( 𝑍𝑛,⊕, ⊙) is the ring of residue classes modulo 𝑛,𝑛≥1, an integer and 𝑁 is the set of nonzero nilpotent elements, is introduced and it is shown that 𝐺(𝑍𝑛,𝑁) can be decomposed into components, for all values of 𝑛 and a method of enumeration of triangles is present. AMS Subject Classification (2010): 05C07, 05C25, 05C30, 05C38, 05C40,16N40, 20F65.

Keywords :Nilpotent elements, Symmetric set, Cayley graph,Nilpotent Cayley graph.

map1 map2 map3