Graph Cores via Universal Completability

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Graph Cores via Universal Completability
Original language description
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
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
—

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)