Povezanost razdaljno-biregularnih grafov / Connectivity of distance-biregular graphs
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Naziv Tittle |
Povezanost razdaljno-biregularnih grafov / Connectivity of distance-biregular graphs |
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Akronim Acronim |
BI-RU/19-20-028 |
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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. |
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Trajanje Duration |
01/01/2019 - 31/12/2021 |
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Vodja projekta Project Leader |
dr. Štefko Miklavič |
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Sodelujoče organizacije Participating organizations |
Faculty of Mechanics and Mathematics, Moscow State University |
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Oddelek Department |
Oddelek za matematiko IAM |