2,235 research outputs found
Oral Interview of John J. Neumaier
No full textJohn J. Neumaier discusses his career, focusing on his time as president of Moorhead State College, from 1958-1968.https://red.mnstate.edu/oral_interviews/1065/thumbnail.jp
Neumaier graphs
No full textA Neumaier graph is an edge-regular graph with a regular clique. Several families of strongly regular graphs (but not all of them) are indeed Neumaier, but in 1981 it was asked whether there are Neumaier graphs that are not strongly regular. This question was only solved a few years ago by Greaves and Koolen, so now we know there are so-called strictly Neumaier graphs. In this talk I will discuss several new results on (strictly) Neumaier graphs, including bounds on the parameters and (non)-existence results obtained in various ways. I will focus on a new construction (involving Cayley graphs) producing an infinite number of strictly Neumaier graphs, but I will also discuss a new Neumaier graph arising from a Latin square. This talk is based on joint research with A. Abiad, W. Castryck, J.H. Koolen and S. Zeijlemaker
Leonore Schwarz Neumaier collection 1909-2002 Bulk dates: 1912-1937
No full textThe collection contains materials about the personal and professional life of opera singer Leonore Schwarz Neumaier (1889-1942), including programs, posters, and correspondence.Two textiles were removed to the LBI Arts and Objects Collection.Leonore Neumaier née Schwarz (1889, Vienna, Austria – 1942, Majdanek camp, Lublin, Poland) pursued her operatic career in Austria and Germany in the early part of the 20th century, singing with opera companies in Graz, Nuremberg, Magdeburg, and Frankfurt am Main, where she was engaged as the first contralto from 1917 to 1921. Following her marriage in 1921 to Otto Neumaier, a Frankfurt businessman, and the birth of their son, Hans (John), she appeared mainly on the concert stage. In the 1930s, the growing repression of German Jews under Nazi-rule restricted her appearances to Jewish groups and organizations associated with the Jüdischer Kulturbund. In June 1942, she was deported from Frankfurt to Majdanek and murdered.Neumaier had shipped most of the material in this collection from Frankfurt to Switzerland in anticipation of immigrating to the United States; the trunks arrived in Minnesota in the early 1950s.Processeddigitize
Neumaier Cayley graphs
No full textA Neumaier graph is a non-complete edge-regular graph with the property that
it has a regular clique. In this paper, we study Neumaier Cayley graphs. We
give a necessary and sufficient condition under which a Neumaier Cayley graph
is a strongly regular Neumaier Cayley graph. We also characterize Neumaier
Cayley graphs with small valency at most .Comment: 17 pages, 1 figur
Neumaier graphs with few eigenvalues
No full textA Neumaier graph is a non-complete edge-regular graph containing a regular clique. In this paper we give some sufficient and necessary conditions for a Neumaier graph to be strongly regular. Further we show that there does not exist Neumaier graphs with exactly four distinct eigenvalues. We also determine the Neumaier graphs with smallest eigenvalue -2
An infinite class of Neumaier graphs and non-existence results
No full textA Neumaier graph is a non-complete edge-regular graph containing a regular clique. A Neumaier graph that is not strongly regular is called a strictly Neumaier graph. In this work we present a new construction of strictly Neumaier graphs, and using Jacobi sums, we show that our construction produces infinitely many instances. Moreover, we prove some necessary conditions for the existence of (strictly) Neumaier graphs that allow us to show that several parameter sets are not admissible
A general construction of strictly Neumaier graphs and a related switching
No full textWe present a construction of Neumaier graphs with nexus 1, which generalises
two known constructions of Neumaier graphs. We also use W. Wang, L. Qiu, and Y.
Hu switching to show that we construct cospectral Neumaier graphs. Finally, we
show that several small strictly Neumaier graphs can be obtained from our
construction, and give a geometric or algebraic description for each of these
graphs
On the existence of small strictly Neumaier graphs
No full textA Neumaier graph is a non-complete edge-regular graph containing a regular
clique. In this work, we prove several results on the existence of small
strictly Neumaier graphs. In particular, we present a theoretical proof of the
uniqueness of the smallest strictly Neumaier graph with parameters
, we establish the existence of a strictly Neumaier graph with
parameters , and we disprove the existence of strictly Neumaier
graphs with parameters , , ,
and . Our proofs use combinatorial techniques
and a novel application of integer programming methods
On the Existence of Small Strictly Neumaier Graphs
No full textA Neumaier graph is a non-complete edge-regular graph containing a regular clique. In this work, we prove several results on the existence of small strictly Neumaier graphs. In particular, we present a theoretical proof of the uniqueness of the smallest strictly Neumaier graph with parameters (16, 9, 4; 2, 4), we establish the existence of a strictly Neumaier graph with parameters (25, 12, 5; 2, 5), and we disprove the existence of strictly Neumaier graphs with parameters (25, 16, 9; 3, 5), (28, 18, 11; 4, 7), (33, 24, 17; 6, 9), (35, 2212; 3, 5), (40, 30, 22; 7, 10) and (55, 34, 18; 3, 5). Our proofs use combinatorial techniques and a novel application of integer programming methods.</p
The smallest strictly Neumaier graph and its generalisations
No full textA regular clique in a regular graph is a clique such that every vertex outside of the clique is adjacent to the same positive number of vertices inside the clique. We continue the study of regular cliques in edge-regular graphs initiated by A. Neumaier in the 1980s and attracting current interest. We thus define a Neumaier graph to be an non-complete edge-regular graph containing a regular clique, and a strictly Neumaier graph to be a non-strongly regular Neumaier graph. We first prove some general results on Neumaier graphs and their feasible parameter tuples. We then apply these results to determine the smallest strictly Neumaier graph, which has 16 vertices. Next we find the parameter tuples for all strictly Neumaier graphs having at most 24 vertices. Finally, we give two sequences of graphs, each with ith element a strictly Neumaier graph containing a 2i-regular clique (where i is a positive integer) and having parameters of an affine polar graph as an edge-regular graph. This answers questions recently posed by G. Greaves and J. Koolen
- …
