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Povezanost razdaljno-biregularnih grafov / Connectivity of distance-biregular graphs

Naziv

Tittle

Povezanost razdaljno-biregularnih grafov / Connectivity of distance-biregular graphs

Akronim

Acronim

BI-RU/19-20-028

Opis

Description

(SI) Naj bo G razdaljno-regularen graf stopnje k, ter naj bo U množica vozlišč grafa G moči k, za katero velja, da G-U ni povezan. V [1] je bilo dokazano tudi, da je v tem primeru množica U enaka množici sosedov nekega vozlišča x grafa G. Podobno je bilo v [2] dokazano, da je vsaka minimalna množica povezav grafa G, brez katerih je graf G nepovezan, enaka množici povezav, ki so incidenčne z nekim vozliščem x grafa G. V tem projektu bomo skušali opisane rezultate za razdaljno-regularne grafe posplošiti na razred razdaljno-biregularnih grafov. [1] A. E. Brouwer in J. H. Koolen, The vertex-connectivity of a distance-regular graph, European J. Combin., 30 (2009), 668-673. [2] A.E. Brouwer i W.H. Haemers, Eigenvalues and perfect matchings, Linear Algebr. Appl., 395 (2005), 155-162.
(EN) Let G be a distance-regular graph with valency k. It was proven in [1] that the only disconnecting sets of vertices of size not more than k are the neighbourhoods of a single vertex of G. Similarly, it was proven in [2] that the only disconnecting sets of edges of G are the sets of edges incident with a single vertex of G In the course of this project we will try to generalize the above results to the class of distance-biregular graphs. [1] A. E. Brouwer and J. H. Koolen, The vertex-connectivity of a distance-regular graph, European J. Combin., 30 (2009), 668-673. [2] A.E. Brouwer and W.H. Haemers, Eigenvalues and perfect matchings, Linear Algebr. Appl., 395 (2005), 155-162.

Trajanje

Duration

01/01/2019 - 31/12/2021

Vodja projekta

Project Leader

dr. Štefko Miklavič

Sodelujoče organizacije

Participating organizations

Faculty of Mechanics and Mathematics, Moscow State University

Oddelek

Department

Oddelek za matematiko IAM
University of Primorska

Andrej Marušič Institute
UP IAM

Muzejski trg 2
6000 Koper
Slovenia

tel.: +386 (0)5 611 75 91
fax.: +386 (0)5 611 75 92
e-mail: info@iam.upr.si
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