##### New appointments

Eric Swartz joined the CMSC as a Research Associate. Eric will be working with John Bamberg and Cai Heng Li.

Stephen Glasby joined the CMSC as a Research Assistant Professor.

Gabriel Verret will be joining the CMSC very soon as a Research Associate on an ARC Discovery Early Career Research Award. Gabriel will be working on 'Enumeration of vertex-transitive graphs'.

We have two new postdoctoral positions open, thanks to our Discovery Project Grants, one with Michael Giudici, and one with John Bamberg, Alice Devillers and Cheryl Praeger. Deadline is February 8th 2013. Details here (positions 4261 and 4262).

##### SymOmega

SymOmega is a mathematical blog run by three CMSC Mathematicians, Michael Giudici, John Bamberg and Gordon Royle.

##### Arxiv

Find in one click all the publications of our members that are deposited on the Arxiv.

##### Conferences

### Early-Career and Mid-Career Researchers Workshop, University of Newcastle, 8-9 December 2012

John Bamberg and Michael Giudici attended and presented talks.

### 36ACCMCC , Sydney, 10-14 December 2012.

This conference was well attended by CMSC members, and we all gave talks:

Brian Corr:"Extending Quokka theory to singular matrices".

Alice Devillers: "Local 2-geodesic transitivity of graphs".

Neil Gillespie: "Completely regular codes with large minimum distance".

Dan Hawtin:"Elusive codes in Hamming graphs".

Irene Pivotto: "Maximum sized binary matroids with no AG(3,2)-minor".

Gordon Royle: "The Merino-Welsh conjecture for series-parallel graphs".

Murray Smith: "Generalising the clique-coclique bound".

### Second Biennial International Group Theory Conference, Istanbul, Turkey, February 4-8 2013.

Cheryl will be a Plenary speaker, she will talk about "Primitive permutation groups containing elements with few cycles".

##### Recent visitors

Bojan Kuzma, 24 November - 2 December 2012, University of Primorska

##### Upcoming visitors

Ferdinand Ihringer, 20 February - 4 April 2013, Justus Liebig Universitat

Leonard Scott, late February for one week, University of Virginia

Padraig O Cathlain, late February for one week, UQ

Jan De Beule, 1 March - 15 April 2013, Universiteit Gent

Andrew Francis, late March for 3 days, UWS

Rudi Pendavingh, 7 April - 17 April 2013, Eindhoven

Peter Nelson, 7 April - 17 April 2013, Victoria University, Wellington

##### News

We have two new postdoctoral positions open, thanks to our Discovery Project Grants, one with Michael Giudici, and one with John Bamberg, Alice Devillers and Cheryl Praeger. Deadline is February 8th 2013. Details here (positions 4261 and 4262).

Gordon Royle and Irene Pivotto went on a research trip to Wellington, NZ, 17-21 December 2012 (for Irene) and 8 - 30 January 2013 for both.

Cheryl Praeger will be working 50% time from January 2013.

Cheryl Praeger received a Citation for outstanding contributions to student learning 2012 from the Australian Government Office for Learning and Teaching.

Cheryl Praeger was an Inaugural Fellow 2012 for the American Mathematical Society.

Cheryl Praeger commences January 2013 as the Vice President, International Commission for Mathematical Instruction 2013-2016 for the International Mathematical Union.

Cheryl Praeger will be part of the International review panel for the DFG Priority Programme: Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory (SPP 1489/2). February 2013, Lambrecht, Germany.

Carmen Amarra has been awarded her PhD for her thesis "Symmetric graphs of diameter two".

Wei Jin has submitted his PhD thesis for examination.

Dan Hawtin has enrolled in a PhD under the supervision of Cheryl Praeger and Neil Gillespie.

Aaron Maynard finished his Honours degree (first-class) on "Extending Burnside's theorem to the infinite case", under Michael Giudici's supervision.

Murray Smith completed Honours (first-class). Murray's thesis was titled "Generalising the clique-Coclique Bound", supervised by John Bamberg.

John supervised a Vacation Scholarship student sponsored by the Head of School. Michael Martis is a second year student who has been doing a project on two-intersection sets of projective space.

Outreach activities: Science Experience with Michael, Alice and Brian; visit from Penrhos College with Alice and Sylvia; National Youth Science Forum with John and Sylvia (session on Coding Theory).

##### Papers

### Published papers

John Bamberg and Nicola Durante, Low dimensional models of the finite split Cayley hexagon, Contemporary Mathematics 579 (2012), 1-20.

Scott Brown, Michael Giudici, Stephen P. Glasby and Cheryl E. Praeger, Proportion of cyclic matrices in maximal reducible matrix algebras. J. Algebra. 369 (2012) 360-368.

Timothy C. Burness, Cheryl E. Praeger and Akos Seress. Extremely primitive sporadic and alternating groups, Bull. London Math. Soc. 44 (2012) 1147-1154.

Alice Devillers, Wei Jin, Cai Heng Li and Cheryl E. Praeger, Local 2-geodesic transitivity and clique graphs, J. Comb. Theory, Series A. 120 (2013) 500-508.

W. W. Fan, D. Lemans, C. H. Li, and J. M. Pan, Locally 2-arc-transitive complete bipartite graphs, J. Combin. Theory Ser. A 120 (2013), 683-699.

Michael Giudici, Geoffrey Pearce and Cheryl E. Praeger, Basic coset geometries, J. Algebraic Combin. 36 (2012) 561-594.

Simon Guest and Cheryl E. Praeger. Proportions of elements with given 2-part order in finite classical groups of odd characteristic, J. Algebra. 372 (2012) 637-660.

Cai Heng Li, Zhe Liu and Zai Ping Lu, The edge-transitive tetravalent Cayley graphs of square-free order. Discrete Math. 312 (2012), no. 12-13, 1952–1967.

Cai Heng Li, Shu-Jiao Song, and Dianjun Wang, Classifying a family of edge-transitive metacirculant graphs. J. Algebraic Combin. 35 (2012), no. 3, 497–513.

Cai Heng Li, Shu-Jiao Song, and Dianjun Wang, A characteriaztion of metacirculants, J. Combin. Theory Ser. A 120 (2013), 39-48.

Cai Heng Li and Hua Zhang, Finite vertex-primitive and vertex-biprimitive 2-path-transitive graphs. J. Algebraic Combin. 36 (2012), no. 2, 231–246.

### Accepted Papers

Alice Devillers, James Parkinson, Hendrik Van Maldeghem, Automorphisms and opposition in twin buildings, accepted in Journal of the Australian Mathematical Society.

Yan Quan Feng, Song Tao Guo and Cai Heng Li, The finite edge-transitive pentavalent graphs, accepted in J. Algebraic Combin.

Yan Quan Feng, Song Tao Guo and Cai Heng Li, The tetravalent edge-primitive graphs, accepted in J. Combin. Theory Ser. B.

Cai Heng Li and Shou Hong Qiao, Finite groups of 4th-power free order, accepted in J. Group Theory.

Cai Heng Li, Shu-Jiao Song, and Dianjun Wang, A family of edge-transitive Frobenius metacirculants, accepted in Europ. J. Combin.

Cai Heng Li, Yanming Wang, Finite groups in which every subgroup is c-normal, accepted in Science China Mathematics.

Cai Heng Li, Jing Xu and Shaohui Sun, Self-complementary circulants of prime-power order, accepted in Siam J. Disc. Math.

Cai Heng Li and Hua Zhang, On finite 2-path-transitive graphs,accepted in J. Graph Theory.

Alice C. Niemeyer, Cheryl E. Praeger and Akos Seress. Estimation problems and randomised group algorithms (Book chapter), accepted in Probabilistic Group Theory, Combinatorics and Computing, Editors: Alla Detinko, Dane Flannery and Eamonn O'Brien. Lecture Notes in Mathematics, Springer, Berlin.

### Submitted papers

Alice Devillers, Michael Giudici, and Cai Heng Li and Cheryl E. Praeger. Locally s-distance transitive graphs and pairwise transitive designs.

Alice Devillers, Wei Jin, Cai Heng Li and Cheryl E. Praeger. On normal 2-geodesic transitive Cayley graphs.

Michael Giudici, Cai Heng Li, Akos Seress and Anne Thomas, Characterising star-transitive and st(edge)-transitive graphs.

Michael Giudici and Chris Parker, There is no upper bound for the diameter of the commuting graphs of a finite group.

Max Neunhoeffer and Cheryl E. Praeger. Sporadic neighbour-transitive codes in Johnson graphs.