# Diameter of Cayley graphs generated by transposition trees

@article{Ganesan2012DiameterOC, title={Diameter of Cayley graphs generated by transposition trees}, author={Ashwin Ganesan}, journal={ArXiv}, year={2012}, volume={abs/1202.5888} }

A problem of practical and theoretical interest is to determine or estimate the diameter of various families of Cayley networks. The previously known estimate for the diameter of Cayley graphs generated by transposition trees is an upper bound given in the oft-cited paper of Akers and Krishnamurthy (1989). In this work, we first assess the performance of their upper bound. We show that for every $n$, there exists a tree on $n$ vertices, such that the difference between the upper bound and the…

## 14 Citations

Bounding the diameter of cayley graphs generated by specific transposition trees

- Mathematics, Computer Science2017 International Conference on Advances in Computing, Communications and Informatics (ICACCI)
- 2017

This article compares various methods for determining an upper bound on the diameter value of a Cayley graph and exact diameters for novel classes of trees are identified.

Upper Bounds for Sorting Permutations with a Transposition Tree

- Computer Science, MathematicsDiscret. Math. Algorithms Appl.
- 2013

For a class of trees, it is proved that the new upper bounds are tighter than β and f(Γ), on average and in most of the cases.

Erratum: "Upper Bounds for Sorting Permutations with a Transposition Tree"

- Computer Science, MathematicsDiscret. Math. Algorithms Appl.
- 2013

The authors' upper bounds are tighter than f(Γ ) and β, on average and in most of the cases, and it is proved that the new upper boundsare tighter than β for a class of trees.

Nonexistence of efficient dominating sets in the Cayley graphs generated by transposition trees of diameter 3

- MathematicsDiscret. Appl. Math.
- 2017

Hardness of Token Swapping on Trees

- Computer Science, MathematicsArXiv
- 2021

This work identifies a broad class of algorithms that encompass all three known polynomial-time algorithms that achieve the best known approximation factor (which is 2) and shows that no such algorithm can achieve an approximation factor less than 2.

The Girth of Cayley graphs of Sylow 2-subgroups of symmetric groups $S_{2^n}$ on diagonal bases

- Mathematics
- 2018

A diagonal base of a Sylow 2-subgroup $P_n(2)$ of symmetric group $S_{2^n}$ is a minimal generating set of this subgroup consisting of elements with only one non-zero coordinate in the polynomial…

Token Swapping on Trees

- Computer Science, MathematicsArXiv
- 2019

A generalized problem---weighted coloured token swapping---is NP-complete on trees, but solvable in polynomial time on paths and stars, and the goal is to get every token to a vertex of the same colour, andThe cost of a swap is the sum of the weights of the two tokens involved.

Better approximation algorithm for point-set diameter

- Computer Science, MathematicsArXiv
- 2018

This work proposes a new $(1+O(\varepsilon)-approximation algorithm with running time of $O(n+ 1/\varpsilon^{\frac{(d-1)}{2}})$ for computing the diameter of a set of points in the d-dimensional Euclidean space for a fixed dimension.

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