7 research outputs found
Eigenvalues, eigenspaces and distances to subsets
AbstractIn this note we show how to improve and generalize some calculations of diameters and distances in sufficiently symmetrical graphs, by taking all the eigenvalues of the adjacency matrix of the graph into account. We present some applications of these results to the problem of finding tight upper bounds on the covering radius of error-correcting codes, when the weight distribution of the code (or the dual code) is known
Graphs with three and four distinct eigenvalues based on circulants
In this paper, we aim to address the open questions raised in various recent
papers regarding characterization of circulant graphs with three or four
distinct eigenvalues in their spectra. Our focus is on providing
characterizations and constructing classes of graphs falling under this
specific category. We present a characterization of circulant graphs with prime
number order and unitary Cayley graphs with arbitrary order, both of which
possess spectra displaying three or four distinct eigenvalues. Various
constructions of circulant graphs with composite orders are provided whose
spectra consist of four distinct eigenvalues. These constructions primarily
utilize specific subgraphs of circulant graphs that already possess two or
three eigenvalues in their spectra, employing graph operations like the tensor
product, the union, and the complement. Finally, we characterize the iterated
line graphs of unitary Cayley graphs whose spectra contain three or four
distinct eigenvalues, and we show their non-circulant nature.Comment: 24 page
The weight distribution of irreducible cyclic codes associated with decomposable generalized Paley graphs
We use known characterizations of generalized Paley graphs which areCartesian decomposable to explicitly compute the spectra of the corresponding associated irreducible cyclic codes. As applications, we give reduction formulas forthe number of rational points in Artin-Schreier curves defined over extension fields and to the computation of Gaussian periods.Fil: Podesta, Ricardo Alberto. Consejo Nacional de Investigaciones Cient铆ficas y T茅cnicas. Centro Cient铆fico Tecnol贸gico Conicet - C贸rdoba. Centro de Investigaci贸n y Estudios de Matem谩tica. Universidad Nacional de C贸rdoba. Centro de Investigaci贸n y Estudios de Matem谩tica; Argentina. Universidad Nacional de C贸rdoba. Facultad de Matem谩tica, Astronom铆a y F铆sica; ArgentinaFil: Videla Guzman, Denis Eduardo. Consejo Nacional de Investigaciones Cient铆ficas y T茅cnicas. Centro Cient铆fico Tecnol贸gico Conicet - C贸rdoba. Centro de Investigaci贸n y Estudios de Matem谩tica. Universidad Nacional de C贸rdoba. Centro de Investigaci贸n y Estudios de Matem谩tica; Argentina. Universidad Nacional de C贸rdoba. Facultad de Matem谩tica, Astronom铆a y F铆sica; Argentin