6 citations · 20 across the 23 of their papers we have counts for
5 papers · 2 filters
Asymptotic enumeration of graphical regular representations
Binzhou Xia, Shasha Zheng
We estimate the number of graphical regular representations (GRRs) of a given group with large enough order. As a consequence, we show that almost all finite Cayley graphs have ful…
Stability of graph pairs involving vertex-transitive graphs
Yan-Li Qin, Binzhou Xia, Sanming Zhou
A pair of graphs is said to be stable if the full automorphism group of is isomorphic to the product of the full automorphism groups of and and unstable…
A solution to Babai's problem on digraphs with non-diagonalizable adjacency matrix
Yuxuan Li, Binzhou Xia, Sanming Zhou +1
The fact that the adjacency matrix of every finite graph is diagonalizable plays a fundamental role in spectral graph theory. Since this fact does not hold in general for digraphs,…
The smallest vertex-primitive -arc-transitive digraph
Fu-Gang Yin, Yan-quan Feng, Binzhou Xia
In 2017, Giudici, Li and the third author constructed the first known family of vertex-primitive -arc-transitive digraphs of valency at least . The smallest digraph in this f…
Aldous' spectral gap property for normal Cayley graphs on symmetric groups
Yuxuan Li, Binzhou Xia, Sanming Zhou
Aldous' spectral gap conjecture states that the second largest eigenvalue of any connected Cayley graph on the symmetric group Sn with respect to a set of transpositions is achieve…