Abstract

Vertex Domination of the Zero-Divisor Cayley Graph of the Residue Class Ring (𝒁𝒏,⨁,⊙)

Levaku Madhavi1*, Jangiti Devendra2 and Tippaluri Nagalakshumma3

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

ABSTRACT

The authors have introduced the notion of zero-divisor Cayley graph associated with the set of zero-divisors in the ring (𝑍𝑛,⨁,⊙) of residue classes modulo 𝑛,𝑛≥1, an integer and studied its properties. In this paper the vertex cover, the vertex dominating set and related properties are studied for this graph. AMS Subject Classification (2010): 05C25, 05C69.

Keywords :Zero-divisor, Symmetric set, Cayley graph, Zero-divisor Cayley graph.

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