Deepa Sinha, Pravin Garg and Anjali Singh

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 17, 2011, Number 3, Pages 49—59

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## Details

### Authors and affiliations

Deepa Sinha

*Centre for Mathematical Sciences, Banasthali University
Banasthali-304022, Rajasthan, India
*

Pravin Garg

*Centre for Mathematical Sciences, Banasthali University
Banasthali-304022, Rajasthan, India
*

Anjali Singh

*Centre for Mathematical Sciences, Banasthali University
Banasthali-304022, Rajasthan, India
*

### Abstract

Let Γ be an abelian group and *B* be a subset of Γ. The addition Cayley graph *G*′ = Cay^{+}(Γ, *B*) is the graph having the vertex set *V* (*G*′) = Γ and the edge set *E*(*G*′) = {*ab* : *a* + *b* ∈ *B*}, where *a*, *b* ∈ Γ. For a positive integer *n* > 1, the unitary addition Cayley graph *G _{n}* is the graph whose vertex set is

*Z*, the integers modulo

_{n}*n*and if

*U*denotes set of all units of the ring

_{n}*Z*, then two vertices a, b are adjacent if and only if

_{n}*a + b ∈ U*. The unitary addition Cayley graph

_{n}*G*is also defined as,

_{n}*G*= Cay

_{n}^{+}(

*Z*,

_{n}*U*). In this paper, we discuss the several properties of unitary addition Cayley graphs and also obtain the characterization of planarity and outerplanarity of unitary addition Cayley graphs.

_{n}### Keywords

- Cayley graph
- Addition Cayley graph
- Unitary Cayley graph
- Unitary addition Cayley graph
- Planar graph

### AMS Classification

- 05C25
- 05C10

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## Cite this paper

Sinha, D., Garg, P., & Singh, A. (2011). Some properties of unitary addition Cayley graphs. Notes on Number Theory and Discrete Mathematics, 17(3), 49-59.