Research

Research interests

• Algebraic graph theory

• Combinatorics

• Group theory

Challenges

1. Prove or disprove: A conjeture on quadratic equations over finite fields of characteristic 3.      I offer 200 AUD for the first correct solution.

2. Give a CFSG-free proof of the result that a connected 3-arc-transitive Cayley graph of odd order is necessarily a cycle.     I offer 100 AUD for the first correct solution.

Published papers

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

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

3. 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.

4. 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.

5. 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.

6. 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.

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

8. 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.

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

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

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

12. 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. 

13. 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.

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

15. 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.

16. 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. 

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

18. 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.

19. 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.

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

21. 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.

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

23. 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.

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

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

26. 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.

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

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

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

30. 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.

31. 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).

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

33. 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.

34. 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.

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

36. 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. 

37. 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".

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

39. 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.

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

41. 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.

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

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

44. 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.

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

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

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

48. 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.

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

50. 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.

51. 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.

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