# On the symmetric digraphs from powers modulo n

@article{Deng2012OnTS, title={On the symmetric digraphs from powers modulo n}, author={Guixin Deng and Pingzhi Yuan}, journal={Discret. Math.}, year={2012}, volume={312}, pages={720-728} }

For any positive integers n and k, let G(n,k) denote the digraph whose set of vertices is H={0,1,2,...,n-1} and there is a directed edge from a@?H to b@?H if a^k=b(modn). The digraph G(n,k) is called symmetric of order M if its set of connected components can be partitioned into subsets of size M with each subset containing M isomorphic components. In this paper, we establish a necessary and sufficient condition for G(n,k) to be symmetric of order M, where M has an odd prime divisor.

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On the symmetric digraphs from the kth power mapping on finite commutative rings

- Mathematics, Computer Science
- Discret. Math. Algorithms Appl.
- 2015

#### References

SHOWING 1-10 OF 15 REFERENCES

On symmetric digraphs of the congruence xk = y (mod n)

- Computer Science, Mathematics
- Discret. Math.
- 2009

The graph of the square mapping on the prime fields

- Computer Science, Mathematics
- Discret. Math.
- 1996

On semiregular digraphs of the congruence x k ≡ y ( mod ) n , Comment

- Math . Univ . Carolin .
- 2007

Power Digraphs M Quart

- Power Digraphs M Quart
- 1998

Power digraphs modulo n

- Fibonacci Quart. 36
- 1998