The following problem is considered: if H is a semiregular abelian subgroup of a transitive permutation group G acting on a finite set X, find conditions for (non)existence of G -invariant partitions of X. Conditions presented in this paper are derived by studying spectral properties of associated G -invariant digraphs. As an essential tool, irreducible complex characters of H are used. Questions of this kind arise naturally when classifying combinatorial objects which enjoy a certain degree of symmetry. As an illustration, a new and short proof of an old result of Frucht et al. (Proc Camb Philos Soc 70:211–218, 1971) classifying edge-transitive generalized Petersen graphs, is given.
COBISS.SI-ID: 1536772036
After giving some basic results, the spectral determination of signed lollipop graphs is considered. It is shown in the paper that any signed lollipop graph is determined by the spectrum of its Laplacian matrix.
COBISS.SI-ID: 1537432004
Irina Elena Cristea published a scientific monograph Fuzzy algebraic hyperstructures (published Springer) in which properties of algebraic structures are generalized to algebraic hyperstructures.
COBISS.SI-ID: 3704571
Janez Žerovnik published a scientific monograph Contribution to environmentally friendly winter road maintenance (published Pearson Education) in which environmentally friendly winter road maintenance is considered.
COBISS.SI-ID: 512610621
Dragan Stevanović published a scientific monograph Spectral Radius of Graphs (published Elsevier) dedicated to developments, proofs, and open problems for spectral graph theory.
COBISS.SI-ID: 1536992708