A5014961672- Advanced Graph Theory Research
- Limits and Structures in Graph Theory
- graph theory and CDMA systems
- Graph theory and applications
- Finite Group Theory Research
- Advanced Combinatorial Mathematics
- Graph Labeling and Dimension Problems
- Computational Geometry and Mesh Generation
- Markov Chains and Monte Carlo Methods
- Interconnection Networks and Systems
- Stochastic processes and statistical mechanics
- Random Matrices and Applications
- Topological and Geometric Data Analysis
- Bayesian Methods and Mixture Models
- Mathematics and Applications
- Coding theory and cryptography
- Graph Theory and Algorithms
- Digital Image Processing Techniques
- Complexity and Algorithms in Graphs
- Advanced Topology and Set Theory
- Rings, Modules, and Algebras
- Matrix Theory and Algorithms
- Algorithms and Data Compression
- Fullerene Chemistry and Applications
- Complex Network Analysis Techniques
Australian National University
2016-2025
Ghent University
2021
University of Mons
2021
KU Leuven
2021
University of Waterloo
1986-2019
Australian Regenerative Medicine Institute
2019
Monash University
2019
Canberra (United Kingdom)
2011
University of Georgia
2005
Rochester Institute of Technology
1994-2004
A new graph product is introduced, and the characteristic polynomial of a so–formed given as function polynomials factor graphs. class trees produced using this shown to be characterized by spectral properties.
Abstract We present the numbers of isotopy classes and main Latin squares, isomorphism quasigroups loops, up to order 10. The best previous results were for squares 8 (Kolesova, Lam, Thiel, 1990 ), 6 (Bower, 2000 loops 7 (Brant Mullen, 1985 ). have been independently found by “QSCGZ” Guérin (unpublished, 2001 also report on most extensive search so far a triple mutually orthogonal (MOLS) Our computations show that any such must only with trivial symmetry groups. © 2006 Wiley Periodicals,...
Consider random regular graphs of order $n$ and degree $d=d(n)\ge 3$. Let $g=g(n)\ge 3$ satisfy $(d-1)^{2g-1}=o(n)$. Then the number cycles lengths up to $g$ have a distribution similar that independent Poisson variables. In particular, we find asymptotic probability there are no with sizes in given set, including girth is greater than $g$. A corresponding result for bipartite graphs.
Abstract Let c ( n, q ) be the number of connected labeled graphs with n vertices and ≤ N = (2 edges. x q/n k − . We determine functions w ˜ 1. a φ( such that e φ )+ uniformly for all ≥ If ϵ > 0 is fixed, → ∞ 4 (1 + ϵ) log , this formula simplifies to exp(– ne −2 ). on other hand, if o 1/2 ), (3/π) /12 /2 (3 −1)/2
An algorithm of Beyer and Hedetniemi [SIAM J. Comput., 9 (1980), pp. 706–712] for generating rooted unlabeled trees is extended to generate free trees. All the nonisomorphic a given size are generated, without repetition, in time proportional number
Abstract The Petersen graph on 10 vertices is the smallest example of a vertex-transitive which not Cayley graph. We consider problem determining orders such graphs. In this, first series papers, we present sequence constructions solve for many orders. particular, graphs exist all divisible by fourth power, and even are square.
We count all latin cubes of order $n\le6$ and hypercubes $n\le5$ dimension $d\le5$. classify these (hyper)cubes into isotopy classes paratopy (main classes). For the same values n d we d-ary quasigroups isomorphism also them according to number identity elements they possess (meaning have counted loops). give an exact formula for (isomorphism of) 3 every d. Then a constructions with specific elements. In process, prove that no 3-ary loop can exactly $n-1$ (but such result holds in dimensions...