Graph Cores via Universal Completability

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10317805" target="_blank" >RIV/00216208:11320/15:10317805 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.sciencedirect.com/science/article/pii/S157106531500092X" target="_blank" >http://www.sciencedirect.com/science/article/pii/S157106531500092X</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.endm.2015.06.046" target="_blank" >10.1016/j.endm.2015.06.046</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Graph Cores via Universal Completability

Popis výsledku v původním jazyce

A framework for a graph G=(V,E), denoted G(p), consists of an assignment of real vectors p=(p1,p2,...,p|V|) to its vertices. A framework G(p) is called universally completable if for any other framework G(q) that satisfies piTpj=qiTqj for i=j and for edges ij there exists an isometry U such that Uqi=pi for all i. A graph is called a core if all its endomorphisms are automorphisms. In this work we identify a new sufficient condition for showing that a graph is a core in terms of the universal completability of an appropriate framework for the graph. To use this condition we develop a method for constructing universally completable frameworks based on the eigenvectors for the smallest eigenspace of the graph. This allows us to recover the known result that the Kneser graph Kn:r and the q-Kneser graph qKn:r are cores for n > = 2r+1. Our proof is simple and does not rely on the use of an Erdős-Ko-Rado type result as do existing proofs. Furthermore, we also show that a new family of graphs

Název v anglickém jazyce

Graph Cores via Universal Completability

Popis výsledku anglicky

A framework for a graph G=(V,E), denoted G(p), consists of an assignment of real vectors p=(p1,p2,...,p|V|) to its vertices. A framework G(p) is called universally completable if for any other framework G(q) that satisfies piTpj=qiTqj for i=j and for edges ij there exists an isometry U such that Uqi=pi for all i. A graph is called a core if all its endomorphisms are automorphisms. In this work we identify a new sufficient condition for showing that a graph is a core in terms of the universal completability of an appropriate framework for the graph. To use this condition we develop a method for constructing universally completable frameworks based on the eigenvectors for the smallest eigenspace of the graph. This allows us to recover the known result that the Kneser graph Kn:r and the q-Kneser graph qKn:r are cores for n > = 2r+1. Our proof is simple and does not rely on the use of an Erdős-Ko-Rado type result as do existing proofs. Furthermore, we also show that a new family of graphs

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Electronic Notes in Discrete Mathematics

ISSN

1571-0653

e-ISSN

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Svazek periodika

49

Číslo periodika v rámci svazku

November

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

8

Strana od-do

337-344

Kód UT WoS článku

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EID výsledku v databázi Scopus

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