Dr. Sanming Zhou


Department of Mathematics and Statistics
The University of Melbourne
Parkville, Victoria 3010, Australia

Room 146, Richard Berry Building
smzhou@ms.unimelb.edu.au
http://www.ms.unimelb.edu.au/~smzhou
Click Here for My Official Web Page
+61 3 8344 3453 (Tel.)
+61 3 8344 4599 (Fax)



Welcome to my personal web page. I was born in China, and I completed my undergraduate and MSc studies there. After receiving my MSc degree I taught mathematics and conducted research in Huazhong (Central China) University of Science and Technology, Wuhan, for a few years before moving to Australia. I received Ph.D. (with distinction) in Algebraic Combinatorics from The University of Western Australia in 2000. Since then I have been working in the Department of Mathematics and Statistics, The University of Melbourne, where I am currently a Senior Lecturer. I am a mathematician working in the broad domain of Discrete Mathematics. My research interests encompass both pure and applied aspects of Discrete Mathematics, including Algebraic Combinatorics, Combinatorial Optimization, Random Graph Processes and Randomized Algorithms, and various network optimization problems from Theoretical Computer Science and Telecommunication. I am the recipient of a 2003 Kirkman Medal, an honour awarded by the International Institute of Combinatorics and Its Applications (ICA) to recognize outstanding work by ICA members in their early research careers. In 2004 I was elected a Fellow of the same organization.

Teaching

Introductory Mathematics (620-161, Semester One, click here to download slides)

Decision Making (620-262, Semester Two)

Network Optimization (620-463, Honours Course, Semester Two)

Administration

I am a joint Honours Coordinator (with Professor Kostya Borovkov) in the Department of Mathematics and Statistics, The University of Melbourne.

Projects for Honours and Ph.D. Students

See my Official Web Page for current and recent Honours and Postgraduate students under my supervision.

It is a lot of fun in doing research on graphs and networks. Tools from algebra (e.g. permutation groups) and probability theory combined with combinatorial techniques have been used widely in solving problems in this field. See below for my research interests and my Official Web Page for a short description of my research areas. If you are interested in doing Honours or Ph.D. in one of these areas, you are welcome to discuss with me. In the following I list two possible topics which suit both Honours and Ph.D. students.

Topic 1: Arc-transitive graphs

A glance at the five Platonic polyhedra will ensure you that they are symmetric in the sense that all edges have the same position. Mathematically, this means that the automorphism group of such a polyhedron as a graph is transitive on its edges, that is, for any two edges there exists a permutation of the vertices which permutes the first edge to the second edge while preserving the structure of the graph. In the language of algebraic graph theory, the 1-skeleton of such a regular polyhedron is an edge-transitive graph. In a similar fashion one can define arc-transitive graphs, where an arc is an oriented edge. The modern study of arc-transitive graphs was initiated by Tutte in his fundamental work in 1940's. Since then it has been one of the central topics in Algebraic Graph Theory. Partly due to the Classification of Finite Simple Groups, a number of beautiful results in this facinating area have been produced by using this powerful tool. In this project you will have opportunities to study those arc-transitive graphs for which a subgroup of the automorphism group is imprimitive on the vertex set. Connections between such graphs and transitive block designs will be emphasized. Students with a strong background in Pure Mathematics, Combinatorics or/and Discrete Mathematics are especially welcome to conduct research in this area.

Topic 2: Combinatorial problems from channel assignment

As suggested by the title, this project is about various combinatorial problems arising from channel assignment in radio communication networks. Typically, such a problem can be formulated as an optimal labelling problem for the underlying graph, and the objective is to minimize a parameter (e.g. the span of the bandwidth) associated with the labelling. Special attention will be paid to graphs with certain type of symmetry.

Research Interests

  1. Algebraic Combinatorics
  2. Network Optimization

  3. Random Graph Processes

Publications

Please comply with all copyright restrictions of relevant journals when accessing and using PDF files of the following publications.

Ph.D. Thesis

  1. S. Zhou, Imprimitive Symmetric Graphs, Ph.D. Thesis, The University of Western Australia, 2000. PDF

Submitted

  1. G. J. Chang, C. Lu and S. Zhou, Minimum spans of Hamming graphs under distance-two labellings, submitted, 17 pages.

  2. A. Thomson and S. Zhou, Gossiping and routing in undirected triple-loop networks, submitted, 17 pages.

  3. S. Zhou, Minimum partition of an independence system into independent sets, submitted, 13 pages.

  4. C. H. Li, C. E. Praeger and S. Zhou, Imprimitive symmetric graphs with cyclic blocks, submitted, 8 pages.

  5. X. Li, V. Mak and S. Zhou, Optimal radio labellings of complete m-ary trees, submitted, 12 pages.

  6. D. King, C. J. Ras and S. Zhou, The L(h, 1, 1)-labelling problem for trees, submitted, 14 pages.

Published (or accepted)

  1. S. Zhou, A class of arc-transitive Cayley graphs as models for interconnection networks, SIAM J. Discrete Math., to appear. PDF

  2. A. Thomson and S. Zhou, Frobenius circulant graphs of valency four, J. Austral. Math. Soc., to appear. PDF

  3. S. Zhou, A distance-labelling problem for hypercubes, Discrete Applied Math., to appear. PDF

  4. S. Zhou, Trivalent 2-arc transitive graphs of type G^1_2 are near polygonal, Annals of Combinatorics, to appear. PDF

  5. S. Zhou, Classification of a family of symmetric graphs with complete 2-arc transitive quotients, Discrete Math., to appear. PDF

  6. S. Zhou, On a class of finite symmetric graphs, European J. Combinatorics 29 (2008), 630-640. PDF

  7. N. C. Wormald and S. Zhou, Large forbidden trade volumes and edge packings of random graphs, Discrete Math. 308 (2008), 2751-2755. PDF

  8. S. Zhou, Distance labelling problems for hypercubes and Hamming graphs - a survey, Electronic Notes in Discrete Mathematics 28 (2007), 527-534. PDF

  9. Z. Lu and S. Zhou, Finite symmetric graphs with 2-arc transitive quotients (II), J. Graph Theory 56 (2007), 167-193. PDF

  10. A. Telcs, N. C. Wormald and S. Zhou, Hamiltonicity of random graphs produced by 2-processes, Random Structures and Algorithms 31 (2007), 450-481. PDF

  11. S. Zhou, Labelling Cayley graphs on abelian groups, SIAM J. Discrete Math. 19 (2006), 985-1003. PDF

  12. S. Zhou, Two-arc transitive near-polygonal graphs, J. A. Bondy et al eds., Graph Theory in Paris, Trends in Mathematics, Birkhauser Verlag, Basel/Switzerland, 2006, pp. 375-380. PDF

  13. G. J. Chang, C. Lu and S. Zhou, No-hole 2-distant colouring for Cayley graphs on finitely generated abelian groups, Discrete Math. 307 (2007), 1808-1817. PDF

  14. J. Yuan, J. Y. Zhang and S. Zhou, Routing permutations and involutions on optical ring networks: complexity results and solution to an open problem, J. Discrete Algorithms 5 (2007), 609-621. PDF

  15. S. Zhou, A local analysis of imprimitive symmetric graphs, J. Algebraic Combinatorics 22 (2005), 435-449. PDF

  16. J. Y. Zhang, Z-Q. Liu and S. Zhou, Dynamic domination in fuzzy causal networks, IEEE Tran. Fuzzy Systems 14 (2006), no.1, 42-57. PDF

  17. S. Zhou, J. Y. Zhang and Z-Q. Liu, Fuzzy causal networks: general model, inference and convergence, IEEE Tran. Fuzzy Systems 14 (2006), no.2, 412-420. PDF

  18. M. A. Iranmanesh, C. E. Praeger and S. Zhou, Finite symmetric graphs with two-arc transitive quotients, J. Combinatorial Theory (B) 94 (2005), 79-99. PDF

  19. S. Zhou, Almost covers of 2-arc transitive graphs, Combinatorica 24 (2004), 731-745. PDF [Erratum: Combinatorica 27 (2007), 745-746. PDF]

  20. J. Yuan and S. Zhou, Polynomial time solvability of the weighted ring arc-loading problem with integer splitting, J. Interconnection Networks 5 (2004), 193-200. PDF

  21. L. Stacho, J. Siran and S. Zhou, Routing balanced communications on Hamiltonian decomposable networks, Parallel Processing Letters 14 (2004), 377-385. PDF

  22. S. Zhou, A Gallai-type equality for the total domination number of a graph, Discuss. Math. Graph Theory 24 (2004), 539-543. PDF

  23. S. Zhou, A channel assignment problem for optical networks modelled by Cayley graphs, Theoretical Computer Science 310 (2004), 501-511. PDF

  24. V. Mak and S. Zhou, Minimum span frequency assignment problem on triangular lattices, in: Proceeding of the 6th International Conference on Optimization: Techniques and Applications (ICOTA6, Ballarat, December 9-11, 2004), 14 pages.

  25. J. Y. Zhang, Z-Q. Liu and S. Zhou, Quotient FCMs: a decomposition theory for fuzzy cognitive maps, IEEE Tran. Fuzzy Systems 11 (2003), 593-604. PDF

  26. S. Zhou, Symmetric graphs and flag graphs, Monatshefte fur Mathematik 139 (2003), 69-81. PDF

  27. S. Zhou, Constructing a class of symmetric graphs, European J. Combinatorics 23(2002), 741-760. PDF

  28. S. Bau, N. C.Wormald and S. Zhou, Decycling numbers of random regular graphs, Random Structures and Algorithms 21 (2002), 397-413. PDF

  29. S. Zhou, Imprimitive symmetric graphs, 3-arc graphs and 1-designs, Discrete Math. 244 (2002), 521-537. PDF

  30. C. H. Li, C. E. Praeger, A. Venkatesh and S. Zhou, Finite locally quasiprimitive graphs, Discrete Math. 246 (2002), 197-218. PDF

  31. M-K. Siu, Z. Zhang and S. Zhou, An inequality between the radius and the inverse dual degree of a tree, Discrete Math. 259 (2002), 351-358. PDF

  32. S. Zhou, Locally restricted colorings of graphs, J. Combin. Math. and Combin. Computing 43 (2002), 147-157. PDF

  33. A. Gardiner, C. E. Praeger and S. Zhou, Cross ratio graphs, J. London Math. Soc. (2) 64 (2001), 257-272. PDF

  34. C. H. Li and S. Zhou, On isomorphisms of minimal Cayley graphs and digraphs, Graphs and Combinatorics 17 (2001), 307-314.

  35. S. Zhou, Classifying a family of symmetric graphs, Bull. Austral. Math. Soc. 63 (2001), 329-335. PDF

  36. C. H. Li, C. E. Praeger and S. Zhou, A class of finite symmetric graphs with 2-arc transitive quotients, Math. Proc. Cambridge Philos. Soc. 129 (2000), 19-34. PDF

  37. S. Zhou, Bounding the bandwidths for graphs, Theoretical Computer Science 249 (2000), 357-368. PDF

  38. S. Zhou, Inequalities involving independence domination, f-domination, connected and total f-domination numbers, Czechoslovak Math. J. 50 (125) (2000), 321-330. PDF

  39. S. Zhou, A sequential coloring algorithm for finite sets, Discrete Math. 199 (1999), 291-297. PDF

  40. B. Chen and S. Zhou, Domination number and neighbourhood conditions, Discrete Math. 195 (1999), 81-91. PDF

  41. S. Zhou, Conditional invariants and interpolation theorems for graphs, J. Combin. Math. and Combin. Computing 30 (1999), 67-89.

  42. S. Zhou, A class of imprimitive symmetric graphs (extended abstract), in: A. Sali, M. Simonovits and V. T. Sos eds., Paul Erdos and His Mathematics (Budapest, 1999), Janos Bolyai Mathematical Society, 1999, pp. 278-280.

  43. S. Zhou and J. Yuan, Harper-type lower bounds and the bandwidths of the compositions of graphs, Discrete Math. 181 (1998), 255-266. PDF

  44. S. Zhou, Interpolation theorems for graphs, hypergraphs and matroids, Discrete Math. 185 (1998), 221-229. PDF

  45. B. Chen and S. Zhou, Upper bounds for f-domination number of graphs, Discrete Math. 185 (1998), 239-243. PDF

  46. S. Zhou, Interpolation theorems for a family of spanning subgraphs, Czechoslovak Math. J. 48 (123) (1998), 45-53. PDF

  47. S. Zhou, Weight distribution of the bases of a binary matroid, Applied Mathematics Letters 11 (1998), 15-18. PDF

  48. S. Zhou, On f-domination number of a graph, Czechoslovak Math. J. 46 (121) (1996), 489-499.

  49. S. Zhou, Matroid tree graphs and interpolation theorems, Discrete Math. 137 (1995), 395-397. PDF

  50. S. Zhou, Unifying approaches for constructing labelled graphs from known ones, J. Combin. Inform. System Sci. 20 (1995), 305-319. PDF

  51. S. Zhou, Several interpolation theorems for graphs, Graph Theory Notes of New York (New York Academy of Sciences) XXIX (1995), 18-20.

  52. S. Zhou and X-N. Yue, Gallai-type equalities for f-domination and connected f-domination numbers, Graph Theory Notes of New York (New York Academy of Sciences) XXIX (1995), 30-32.

  53. J. Yuan and S. Zhou, Optimal labelling of unit interval graphs, Appl. Math. J. Chinese Univ. Ser. B (English edition) 10 (1995), 337-344. PDF

  54. S. Zhou, Interpolation theorems for the f-chromatic index of multigraphs, in: Y. Alavi, D. R. Lick and J. Liu eds., Combinatorics, Graph Theory, Algorithms and Applications, World Scientific Publishing, River Edge, NJ, 1994, pp. 433-438.

  55. S. Zhou, Disjoint hamiltonian cycles in Fan-2k type graphs, J. Graph Theory 17 (1993), 673-678. PDF

Last Update: July 10, 2008
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