Searcharxiv⌕ Search

arXiv subjects

Jozef Siran

Publications and source records attributed to Jozef Siran.

3 recordsLinked to original sources
arXiv2023

Orientably-regular embeddings of complete multigraphs

An embedding of a graph on an orientable surface is orientably-regular (or rotary, in an equivalent terminology) if the group of orientation-preserving automorphisms of the embedding is transitive (and hence regular) on incident vertex-edge pairs of the graph. A classification of orientably-regular embeddings of complete graphs was obtained by L. D. James and G. A. Jones [in "Regular orientable imbeddings of complete graphs", J. Combinatorial Theory Ser. B 39 (1985), 353-367], pointing out interesting connections to finite fields and Frobenius groups. By a combination of graph-theoretic methods and tools from combinatorial group theory we extend results of James and Jones to classification of orientably-regular embeddings of complete multigraphs with arbitrary edge-multiplicity.

math.CO↗
arXiv2023

Extreme and statistical properties of eigenvalue indices of simple connected graphs

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 multipartite graphs. We also present results on density of spectral gap indices and its nonpersistency with respect to small perturbations of the underlying graph. We show that a small change in the set set of edges may result in a significant change of the spectral index like, e.g., the spectral gap or spectral index. We also present a statistical and numerical analysis of spectral indices of graphs of the order $m\le 10$. We analyze the extreme values for spectral indices for graphs and their small perturbations. Finally, we present the statistical and extreme properties of graphs on $m\le 10$ vertices.

math.CO↗