8 papers · 1 filter
Extreme and statistical properties of eigenvalue indices of simple connected graphs
Sona Pavlikova, Daniel Sevcovic, Jozef Siran
We analyze graphs attaining the extreme values of various spectral indices in the class of all simple connected graphs, as well as in the class of graphs which are not complete mul…
Classifying edge-biregular maps of negative prime Euler characteristic
Olivia Jeans, Jozef Širáň
An edge-biregular map arises as a smooth normal quotient of a unique index-two subgroup of a full triangle group acting with two edge-orbits. We give a classification of all finite…
On the upper embedding of Steiner triple systems and Latin squares
Terry S. Griggs, Thomas A. McCourt, Jozef Siran
It is proved that for any prescribed orientation of the triples of either a Steiner triple system or a Latin square of odd order, there exists an embedding in an orientable surface…
On the upper embedding of symmetric configurations with block size 3
Grahame Erskine, Terry Griggs, Jozef Širáň
We consider the problem of embedding a symmetric configuration with block size 3 in an orientable surface in such a way that the blocks of the configuration form triangular faces a…
Graphs derived from perfect difference sets
Grahame Erskine, Peter Fratrič, Jozef Širáň
We study a family of graphs with diameter two and asymptotically optimal order for their maximum degree, obtained from perfect difference sets. We show that for all known examples…
Spectra and eigenspaces of arbitrary lifts of graphs
C. Dalfó, M. A. Fiol, S. Pavlíková +1
We describe, in a very explicit way, a method for determining the spectra and bases of all the corresponding eigenspaces of arbitrary lifts of graphs (regular or not).