Seminár z teórie grafov - Primož Šparl (27.10.2016)

vo štvrtok 27.10.2016 o 9:50 hod. v miestnosti M/213

24. 10. 2016 09.34 hod.
Od: Martin Škoviera

Prednášajúci: Primož Šparl (University of Ljubljana)

Názov: On n-distance-balanced graphs

Termín: 27.10.2016, 9:50 hod., M/213

Abstrakt:
Distance-balanced graphs (that is graphs in which for every pair of adjacent vertices u and v the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u) have been studied to some extent in recent years, investigating different structural properties of such graphs and also the connection of this property to symmetries of graphs. In this talk we present a very natural generalization of the concept of distance-balanced graphs to so-called n-distance-balanced graphs, which was first introduced by Boštjan Frelih in 2014. We discuss some basic properties of n-distance-balanced graphs, give examples of such graphs and present a characterization of such graphs of small diameter. We also discuss the n-distance-balanced property for some well-known families of graphs such as the family of generalized Petersen graphs and pose a number of open problems. This is joint work with Štefko Miklavič.