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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433

Rev. Mat vol.25 n.1 San José Jan./Jun. 2018

http://dx.doi.org/10.15517/rmta.v1i25.32228 

Artículos

On Delta-Graphs And Delta Conjecture

Sobre Delta-Grafos Y La Conjetura Delta

Pedro Díaz Navarro1 

1Escuela de Matemática, Universidad de Costa Rica, San José, Costa Rica. E-Mail: pdiaz@costarricense.cr; pdiazn@gmail.com

Abstract

In this paper we define two infinite families of graphs called C-δ graphs and δ-graphs and prove that δ-graphs satisfy delta conjecture. Also we see that C-δ graphs family contains the complements of δ-graphs. Finally we give a list of C-δ graphs and the relationship with the minimum semidefinite rank of these graphs.

Keywords: delta conjecture; simple connected graphs; minimum semidefinite rank; δ-graph; C-δ graphs; orthogonal representation.

Resumen

En este artículo definimos dos familias de grafos llamadas C-δ grafos y δ-grafos y se prueba que los δ-grafos satisfacen la conjetura delta. También vemos que la familia de los C-δ grafos contienen los complementos de los δ-grafos. Finalmente damos una lista de C-δ grafos y la relación con el rango mínimo semidefinido de estos grafos.

Palabras clave: conjetura delta; grafo simple conexo; rango mínimo semidefinido; δ-grafo; C-δ grafo; representación ortogonal

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Received: October 18, 2016; Revised: October 09, 2017; Accepted: October 17, 2017

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