Algebraic Graph Theory
The Laplacian of a Graph and Cuts and Flows are compared to the Rank Polynomial.
Matroids with nine elements
- Dillon Mayhew, G. Royle
- MathematicsJournal of combinatorial theory. Series B (Print)
- 12 February 2007
Computing Tutte Polynomials
- G. Haggard, David J. Pearce, G. Royle
- Mathematics, Computer ScienceACM Transactions on Mathematical Software
- 1 September 2010
The implementation of a program that exploits isomorphisms in the computation tree to extend the range of graphs for which it is feasible to compute their Tutte polynomials is described and the utility of the program is demonstrated by finding counterexamples to a conjecture of Welsh on the location of the real flow roots of a graph.
Flocks and ovals
- W. Cherowitzo, Tim Penttila, I. Pinneri, G. Royle
- Mathematics
- 1 March 1996
An infinite family of q-clans, called the Subiaco q-clans, is constructed for q=2e. Associated with these q-clans are flocks of quadratic cones, elation generalized quadrangles of order (q2, q),…
Symmetric squares of graphs
- K. Audenaert, C. Godsil, G. Royle, T. Rudolph
- MathematicsJournal of combinatorial theory. Series B (Print)
- 12 July 2005
Small graphs with chromatic number 5: A computer search
- Tommy R. Jensen, G. Royle
- MathematicsJournal of Graph Theory
- 1995
In this article we give examples of a triangle-free graph on 22 vertices with chromatic number 5 and a K4-free graph on 11 vertices with chromatic number 5. We very briefly describe the computer…
Sets of type (m, n) in the affine and projective planes of order nine
- Tim Penttila, G. Royle
- MathematicsDes. Codes Cryptogr.
- 1 November 1995
The results of exhaustive computer searches for sets of points of type (m, n) in the projective and affine planes of order nine are given, leading to the conclusion that sets of types are far more numerous than was previously thought.
Chromatic Number and the 2-Rank of a Graph
We show that if the adjacency matrix of a graph X has 2-rank 2r, then the chromatic number of X is at most 2r+1, and that this bound is tight.
Cores of Geometric Graphs
Cameron and Kazanidis have recently shown that rank-three graphs are either cores or have complete cores, and they asked whether this holds for all strongly regular graphs. We prove that this is true…
...
...