Ghent University

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Showing 2018 · math.COShow all

6 papers · 2 filters

math.CO2018★ 14 cited

Graphs with few Hamiltonian Cycles

Jan Goedgebeur, Barbara Meersman, Carol T. Zamfirescu

We describe an algorithm for the exhaustive generation of non-isomorphic graphs with a given number $k \geq 0$ of hamiltonian cycles, which is especially efficient for small $k$ . Ou…

math.CO2018

New and Updated Semidefinite Programming Bounds for Subspace Codes

Daniel Heinlein, Ferdinand Ihringer

We show that $A_{2} (7, 4) \leq 388$ and, more generally, $A_{q} (7, 4) \leq (q^{2} - q + 1) [7]_{q} + q^{4} - 2 q^{3} + 3 q^{2} - 4 q + 4$ by semidefinite programming for $q \leq 101$ . Furthermore, we exte…

math.CO2018

A characterization and an application of weight-regular partitions of graphs

Aida Abiad

A natural generalization of a regular (or equitable) partition of a graph, which makes sense also for non-regular graphs, is the so-called weight-regular partition, which gives to…

math.CO2018★ 3 cited

Bounds for the smallest $k$ -chromatic graphs of given girth

Geoffrey Exoo, Jan Goedgebeur

Let $n_{g} (k)$ denote the smallest order of a $k$ -chromatic graph of girth at least $g$ . We consider the problem of determining $n_{g} (k)$ for small values of $k$ and $g$ . After giving…

math.CO2018★ 4 cited

Opposition diagrams for automorphisms of small spherical buildings

J. Parkinson, H. Van Maldeghem

An automorphism $θ$ of a spherical building $Δ$ is called \textit{capped} if it satisfies the following property: if there exist both type $J_{1}$ and $J_{2}$ simplices of $Δ$ mapped o…

math.CO2018★ 1 cited

Graph switching, 2-ranks, and graphical Hadamard matrices

Aida Abiad, Steve Butler, Willem H. Haemers

We study the behaviour of the 2-rank of the adjacency matrix of a graph under Seidel and Godsil-McKay switching, and apply the result to graphs coming from graphical Hadamard matri…