Research

Research interests

• Graph symmetry

• Algebraic combinatorics

• Permutation group theory

Challenges

1. Prove or disprove: A conjeture on quadratic equations over finite fields of characteristic 3.     

2. Give a CFSG-free proof of the result that a connected 3-arc-transitive Cayley graph of odd order is necessarily a cycle.    

Published papers

1. Yuan-Dong Li, Binzhou Xia and Jin-Xin Zhou, On automorphism groups of half-arc-transitive tetravalent graphs, European J. Combin., 137 (2026), Paper No. 104416, 9 pp. ArXiv

2. Teng Fang and Binzhou Xia, Tiling the symmetric group by transpositions, Bull. Lond. Math. Soc., 58 (2026), no. 5, Paper No. e70366, 16 pp. ArXiv

3. Yunsong Gan, Weijun Liu and Binzhou Xia, On biprimitive semisymmetric graphs, J. Algebra, 692 (2026), 422–462. ArXiv

4. Jiyong Chen, Đorđe Mitrović, Melissa Lee, E. A. O'Brien and Binzhou Xia, Elusive groups from non-split extensions, J. Pure Appl. Algebra, 230 (2026), no. 4, Paper No. 108228, 18 pp. ArXiv

5. Xu Cheng Bu, Jing Jian Li and Binzhou Xia, Cayley digraphs of direct products of finite simple groups with out-valency two, Comm. Algebra, 54 (2026), no. 5, 2216–2225.

6. Binzhou Xia, Zhishuo Zhang and Sanming Zhou, Determining the vertex stabilizers of 4-valent half-arc-transitive graphs, J. Algebra, 688 (2026), 307–343. ArXiv

7. Yuxuan Li, Binzhou Xia and Sanming Zhou, The second largest eigenvalue of some nonnormal Cayley graphs on symmetric groups, J. Combin. Theory Ser. A, 218 (2026), Paper No. 106097, 30 pp. ArXiv

8. Jia-Li Du, Yan-Quan Feng, Binzhou Xia and Da-Wei Yang, The existence of m-Haar graphical representations, J. Combin. Theory Ser. A, 218 (2026), Paper No. 106096, 30 pp. ArXiv

9. Yunsong Gan, Pablo Spiga and Binzhou Xia, Asymptotic enumeration of Haar graphical representations, Combinatorica, 45 (2025), no. 5, Paper No. 51, 43 pp. ArXiv

10. Junyan Chen, Lei Chen, Michael Giudici, Jing Jian Li, Cheryl Praeger and Binzhou Xia, Bounding s for vertex-primitive s-arc-transitive digraphs of alternating and symmetric groups, Ars Math. Contemp., 25 (2025), no. 4, Paper No. 1, 15 pp. Arxiv

11. Jinhua Xie, Yan-Quan Feng and Binzhou Xia, Generalized quaternion groups with the m-DCI property, Electron. J. Combin., 32 (2025), no. 2, Paper No. 2.47, 18 pp. ArXiv

12. Yunsong Gan, Weijun Liu and Binzhou Xia, Unexpected automorphisms in direct product graphs, J. Combin. Theory Ser. B, 171 (2025), 140–164. ArXiv

13. Binzhou Xia, Graphical regular representations of  (2,p)-generated groups, European J. Combin. 124 (2025), Paper No. 104058, 12 pp. Arxiv

14. Binzhou Xia, Junyang Zhang, Zhishuo Zhang and Wenying Zhu, A complete classification of shuffle groups, Forum Math. Sigma, 12 (2024), Paper No. e104, 16 pp. ArXiv

15. Yuxuan Li, Binzhou Xia and Sanming Zhou, The second largest eigenvalue of normal Cayley graphs on symmetric groups generated by cycles, J. Combin. Theory Ser. A 206 (2024), Paper No. 105885, 32 pp. ArXiv

16. Yuxuan Li, Binzhou Xia, Sanming Zhou and Wenying Zhu, A solution to Babai's problems on digraphs with non-diagonalizable adjacency matrix, Combinatorica 44 (2024), no. 1, 179–203. ArXiv

17. Yan-Li Qin, Binzhou Xia and Sanming Zhou, Stability of graph pairs involving vertex-transitive graphs, Discrete Math. 347 (2024), no. 4, Paper No. 113856, 6 pp. ArXiv

18. Binzhou Xia and Shasha Zheng, Asymptotic enumeration of graphical regular representations, Proc. Lond. Math. Soc. (3) 127 (2023), no. 5, 1424–1450. ArXiv

19. Cai Heng Li, Lei Wang and Binzhou Xia, The exact factorizations of almost simple groups, J. Lond. Math. Soc. (2) 108 (2023), no. 4, 1417–1447. ArXiv

20. Teng Fang, Binzhou Xia, Shasha Zheng and Sanming Zhou, Cubic graphical regular representations of Ree groups, Comm. Algebra, 51 (2023), no. 9, 3729–3733. 

21. Yanpeng Wang, Binzhou Xia and Sanming Zhou, Regular sets in Cayley graphs, J. Algebraic Combin., 57 (2023), no. 2, 547–558.   ArXiv

22. Fu-Gang Yin, Yan-Quan Feng and Binzhou Xia, The smallest vertex-primitive 2-arc-transitive digraph, J. Algebra, 626 (2023), 1–38.   ArXiv

23. Binzhou Xia, New necessary conditions for the existence of finite non-Desarguesian flag-transitive projective planes, European J. Combin., 110 (2023), Paper No. 103687, 14 pp.  ArXiv

24. Yuxuan Li, Binzhou Xia and Sanming Zhou, Aldous' spectral gap property for normal Cayley graphs on symmetric groups, European J. Combin., 110 (2023), Paper No. 103657, 16 pp. ArXiv

25. Binzhou Xia, Shasha Zheng and Sanming Zhou, Cubic graphical regular representations of some classical simple groups, J. Algebra, 612 (2022), 256–280.  ArXiv

26. Jiangmin Pan, Binzhou Xia and Fugang Yin, 2-arc-transitive Cayley graphs on alternating groups, J. Algebra, 610 (2022), 655–683. Corrigendum: on Page 663, Line 7, HM/H should be HM/M. ArXiv

27. Cai Heng Li and Binzhou Xia, Factorizations of almost simple groups with a solvable factor, and Cayley graphs of solvable groups, Mem. Amer. Math. Soc., 279 (2022), no. 1375, v+99 pp. ISBN: 978-1-4704-5383-1; 978-1-4704-7229-0. Corrigendum: in the proof of Lemma 8.31, row 8 of Table 1.1 with q=2 should have been considered, although it is easy to exclude this case---the normalizer of L_{\alpha\beta} in L is contained in L_\alpha.  ArXiv

28. Yanpeng Wang , Binzhou Xia and Sanming Zhou, Subgroup regular sets in Cayley graphs, Discrete Math., 345 (2022), no. 11, Paper No. 113023, 9 pp. ArXiv

29. Jing Jian Li, Binzhou Xia, Xiao Qian Zhang and Shasha Zheng, Cubic graphical regular representations of PSU3(q), Discrete Math., 345 (2022), no. 10, Paper No. 112982, 10 pp. ArXiv

30. Gabriel Verret and Binzhou Xia, Oriented regular representations of out-valency two for finite simple groups, Ars Math. Contemp., 22 (2022), no. 1, Paper No. 7, 6 pp. ArXiv

31. Cai Heng Li, Jiangmin Pan and Binzhou Xia, Finite quasiprimitive permutation groups with a metacyclic transitive subgroup, J. Algebra, 588 (2021), 250–277. ArXiv

32. Yan-Li Qin, Binzhou Xia and Sanming Zhou, Canonical double covers of generalized Petersen graphs, and double generalized Petersen graphs, J. Graph Theory, 97 (2021), no. 1, 70–80. ArXiv

33. Cai Heng Li, Binzhou Xia and Sanming Zhou, An explicit characterization of arc-transitive circulants, J. Combin. Theory Ser. B, 150 (2021), 1–16. ArXiv

34. Pablo Spiga and Binzhou Xia, Constructing infinitely many half-arc-transitive covers of tetravalent graphs, J. Combin. Theory Ser. A, 180 (2021), 105406, 16 pp. ArXiv

35. Binzhou Xia, Tetravalent half-arc-transitive graphs with unbounded nonabelian vertex stabilizers, J. Combin. Theory Ser. B, 147 (2021), 159–182.         Magma codes. ArXiv

36. Yan-Li Qin, Binzhou Xia, Jin-Xin Zhou and Sanming Zhou, Stability of graph pairs, J. Combin. Theory Ser. B, 147 (2021), 71–95.

37. Alice Devillers, Hongxue Liang, Cheryl E. Praeger and Binzhou Xia, On flag-transitive 2-(v,k,2) designs, J. Combin. Theory Ser. A, 177 (2021), 105309, 45 pp. ArXiv

38. Binzhou Xia, On cubic graphical regular representations of finite simple groups, J. Combin. Theory Ser. B, 141 (2020), 1–30. ArXiv

39. Jiyong Chen, Yanpeng Wang and Binzhou Xia, Characterization of subgroup perfect codes in Cayley graphs, Discrete Math., 343 (2020), no. 5, 111813.  ArXiv

40. Binzhou Xia, Cubic graphical regular representations of PSL3(q), Discrete Math., 343 (2020), no. 1, 111646. 

41. Michael Giudici, Cai Heng Li and Binzhou Xia, Vertex-primitive s-arc-transitive digraphs of linear groups, J. Pure Appl. Algebra, 223 (2019), no. 12, 5455–5483. ArXiv

42. Cai Heng Li and Binzhou Xia, Factorizations of almost simple groups with a factor having many nonsolvable composition factors, J. Algebra, 528 (2019), 439–473.          Corrigendum: In Table~1, the triple (L,H \cap L,K \cap L)=(Sp_6(4),(Sp_2(4) \times Sp_2(16)).2,G_2(4)) is missing, and for the first two rows R.2 should be R.P with P \leqslant 2. In Example 3.5, Sp_{4\ell-2}(q) should be \Omega_{4\ell-1}(q). ArXiv

43. Yan-Li Qin, Binzhou Xia and Sanming Zhou, Stability of circulant graphs, J. Combin. Theory Ser. B, 136 (2019), 154–169. ArXiv

44. S.P. Glasby, Cheryl E. Praeger and Binzhou Xia, ‘Norman involutions’ and tensor products of unipotent Jordan blocks, Israel J. Math., 230 (2019), no. 1, 153–181. ArXiv

45. John Bamberg, Cheryl E. Praeger and Binzhou Xia, The covering radii of the 2-transitive unitary, Suzuki, and Ree groups, J. Group Theory, 22 (2019), no. 1, 103–117. ArXiv

46. Binzhou Xia, Cyclotomic difference sets in finite fields, Math. Comp., 87 (2018) no. 313, 2461–2482. ArXiv

47. Jiyong Chen, Binzhou Xia and Jin-Xin Zhou, An infinite family of cubic nonnormal Cayley graphs on nonabelian simple groups, Discrete Math., 341 (2018) no. 5, 1282–1293.           Corrigendum: On page 1284, line 5, "(gh)" should be "(hg)". On page 1292, line 5, "by both xzx and z" should be "by both xyx and y". On the second last line in the proof of Lemma 4.4, a term -1 is missing before the last equality.  ArXiv

48. He Huang, Binzhou Xia and Sanming Zhou, Perfect codes in Cayley graphs, SIAM J. Discrete Math., 32 (2018) no. 1, 548–559.          Corrigendum: The two sentences in the last line of page 553 and the first line of 554 should be "If n/t is odd, then we have (gh)^2=e with h:=g^{n/t-1}\in H". ArXiv

49. Michael Giudici and Binzhou Xia, Vertex-quasiprimitive 2-arc-transitive digraphs, Ars Math. Contemp., 14 (2018) no. 1, 67–82. ArXiv

50. Michael Giudici, Cai Heng Li and Binzhou Xia, An infinite family of vertex-primitive 2-arc-transitive digraphs, J. Combin. Theory Ser. B, 127 (2017), 1–13. ArXiv

51. Binzhou Xia, Quasiprimitive groups containing a transitive alternating group, J. Algebra, 490 (2017), 555–567. ArXiv

52. Teng Fang, Xin Gui Fang, Binzhou Xia and Sanming Zhou, Vertex-imprimitive symmetric graphs with exactly one edge between any two distinct blocks, J. Combin. Theory Ser. A, 152 (2017), 303–340. ArXiv

53. Binzhou Xia, The covering radius of PGL2(q), Discrete Math., 340 (2017) no. 10, 2469–2471.

54. Binzhou Xia and Teng Fang, Cubic graphical regular representations of PSL2(q), Discrete Math., 339 (2016) no. 8, 2051–2055. ArXiv

55. Teng Fang, Xin Gui Fang, Binzhou Xia and Sanming Zhou, A family of symmetric graphs with complete quotients, Electron. J. Combin., 23 (2016) no. 2, P2.27.

56. Jing Chen and Binzhou Xia, On isomorphisms of vertex-transitive graphs, Electron. J. Combin., 23 (2016) no. 2, P2.22. ArXiv

57. S.P. Glasby, Cheryl E. Praeger and Binzhou Xia, Decomposing modular tensor products, and periodicity of ‘Jordan partitions’, J. Algebra, 450 (2016), 570–587. ArXiv

58. Mengyang Gu, Zhiyi Tan, Binzhou Xia and Yujie Yan, A new approach for bicriteria partitioning problem, Optim. Lett., 9 (2015), 1025–1037.

59. S. P. Glasby, Cheryl E. Praeger and Binzhou Xia, Decomposing modular tensor products: ‘Jordan partitions’, their parts and p-parts, Israel J. Math., 209 (2015) no.1, 215–233. ArXiv

60. Binzhou Xia and Tianxin Cai, A new kind of Diophantine equations, Acta Arith., 147 (2011) no. 3, 245–251.

61. Binzhou Xia and Zhiyi Tan, Tighter bounds of the first fit algorithm for the bin-packing problem, Discrete Appl. Math., 158 (2010) no. 15, 1668–1675.

62. Binzhou Xia and Tianxin Cai, Bernoulli numbers and congruences for harmonic sums, Int. J. Number Theory, 6 (2010) no. 4, 849–855.           Corrigendum: There is a typo on page 851, where the numerator in the second line should have been 1 instead of n.

63. Binzhou Xia and Tianxin Cai, Alternating Mordell-Tornheim and Witten multiple series (in Chinese), Sci. Sin. Math., 40 (2010) no. 6, 517–532.