On Cayley representations of central Cayley graphs over almost simple groups
Jin Guo, Wenbin Guo, Grigory Ryabov, Andrey V. Vasil'ev

TL;DR
This paper investigates the uniqueness and enumeration of Cayley representations of central Cayley graphs over simple and almost simple groups, providing theoretical bounds and an efficient algorithm for their classification.
Contribution
It proves bounds on the number of Cayley representations over simple groups and introduces a polynomial-time algorithm for classifying all representations over almost simple groups.
Findings
Central Cayley graphs over simple groups have at most two nonequivalent representations.
An algorithm is provided to find all representations over almost simple groups with bounded socle index.
The algorithm runs in polynomial time relative to the size of the group.
Abstract
A Cayley graph over a group is said to be central if its connection set is a normal subset of . We prove that every central Cayley graph over a simple group has at most two pairwise nonequivalent Cayley representations over associated with the subgroups of induced by left and right multiplications of . We also provide an algorithm which, given a central Cayley graph over an almost simple group whose socle is of a bounded index, finds the full set of pairwise nonequivalent Cayley representations of over in time polynomial in size of .
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Taxonomy
TopicsFinite Group Theory Research · graph theory and CDMA systems · Coding theory and cryptography
