This is the University of Auckland home page for Dr. Eyal Loz.

Eyal Loz has successfully completed his PhD at the University of Auckland, with a thesis on "The Degree-Diameter and Cage Problems: A Study in Structural Graph Theory" (written under the supervision of Jozef Siran and Marston Conder). Eyal used covering and voltage graph techniques to construct many of what are now the largest known connected regular graphs of given degree d and diameter k, for d up to 20 and k up to 10.

During his PhD studies Eyal recived the Top Achiever Doctoral Scholarship from the New Zealand Tertiary Education Commission (NZTEC) and also as appointment as postgraduate scholar to Combinatorics programme of the New Zealand Institute of Mathematics & its Applications (NZIMA).

Teaching:

2008:

• Lecturer and Course Coordinator for MATHS 326 (Combinatorial Computing).
• Lecturer for sections of MATHS 715 (Graph Theory and Combinatorics).

2007:

• Lecturer and Course Coordinator for MATHS 326 (Combinatorial Computing).
• Lecturer for sections of MATHS 715 (Graph Theory and Combinatorics).

2006:

• Lecturer for sections of MATHS 714 (Number Theory) and MATHS 715 (Graph Theory and Combinatorics).
• Head Tutor for MATHS 326 (Combinatorial Computing), COMPSCI 320 (Algorithmics) and COMPSCI 225 (Discrete Structures).

Publications:

• Eyal Loz and Guillermo Pineda-Villavicencio, New benchmarks for large scale networks with given maximum degree and diameter. The Computer Journal. Oxford University Press. The British Computer Society. Accepted.
• E. Loz, M. Miller, J. Siagiova, J. Siran and Jana Tomanova, Re-visiting constructions of small regular graphs of girth 5 and 6: Vertex-transitive and Cayley graphs. Submitted.
• Eyal Loz, Graphs of given degree and diameter obtained as abelian lifts of dipoles. Discrete Mathematics 309 (2009) 3125--3130.
• Eyal Loz and Jozef Siran, New record graphs in the degree-diameter problem. Australasian Journal of Combinatorics. Volume 41 (2007), p.63

Conferences and international visits:

2008:

• Conference Presentation, The Fourth International Conference on Combinatorial Mathematics and Combinatorial Computing (4ICC), University of Auckland, December.
• Conference Presentation, GTA'08 Workshop, University of Newcastle, Australia, December.
• Six month visit to the Graph Theory and Applications Research Group (GTA), Department of Computer Science, University of Newcastle, hosted by Prof. Mirka Miller.

2007:

• Six month visit to Slovak Institute of Technology, hosted by Prof. Jozef Siran.
• Invited Speaker, Bratislava Graph Theory Seminar, Comenius University, September.
• Invited Speaker, International Workshop on Optimal Network Topologies (IWONT-2007), Czech Republic, September.
• Conference Presentation, 6th Slovenian International Conference on Graph Theory, Bled (Slovenia), June.

2006:

• Presentation in the Department of Mathematics Seminar Series, University of Auckland.
• Invited Speaker, Biomathematics Unit Seminar series, Department of Zoology, Tel Aviv University, Israel, January.

Links:

• A link to Dr. Eyal Loz's Personal Home Page.
• A link to Combinatorics Wiki.