de Matematicas Discrretas
El principal objetivo del Seminario Preguntón es dar a conocer las diferentes líneas de investigación, dentro de las matemáticas discretas, que se trabajan en todo el país (particularmente en Querétaro) como proyectos de tesis doctorales o estancias posdoctorales. En el Seminario Preguntón se propone fomentar el intercambio de ideas y conocimiento para fortalecer los proyectos de todos los participantes.
Organizadores: Dr. Luis Montejano y Dr. Isaac Arelio
Viernes 11 de Abril de 2025
13:00 - 14:00 hrs
Some new types of graph regularities and finite geometries
György Kiss
ELTE, Budapest (Hungary) & University of Primorska, Koper (Slovenia)
In this talk we consider some new types of graph regularities (girth-regular, edge-girth-regular, vertex-girth-regular) and their connections to finite geometries. Let Γ denote a simple, connected, finite k-regular graph. For an edge of Γ let n(e) denote the number of girth cycles containing e. For a vertex v of Γ let { e1, e2, ..., ek } be the set of edges incident to v ordered such that n( e1 ) ≤ n( e2 ) ≤ ... ≤ n( ek ). Then (n( e1 ), n( e2 ), ..., n( ek )) is called the signature of v. The graph Γ is said to be girth-regular if all of its vertices have the same signature. Γ is called edge-girth-regular, if n( e1 ) = n( e2 ) = ... = n( ek ) for all vertices, and it is called vertex-girth-regular, if any vertex lies on the same number of girth cycles (the sum n( e1 ) + n( e2 ) + ... + n( ek ) = λ for all vertices of Γ). We show that girth-regular graphs are related to cages, finite projective and affine spaces and generalized polygons.