Adjacency matrices of polarity graphs and of other C4-free graphs of large size

All of RECERCAT

To access the full text documents, please follow this link: http://hdl.handle.net/2117/8737

Title:	Adjacency matrices of polarity graphs and of other C4-free graphs of large size
Author:	Abreu, M.; Balbuena Martínez, Maria Camino Teófila; Labbate, D.
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
Abstract:	In this paper we give a method for obtaining the adjacency matrix of a simple polarity graph $G_q$ from a projective plane PG(2,q), where q is a prime power. Denote by ex(n;C₄) the maximum number of edges of a graph on n vertices and free of squares C₄. We use the constructed graphs $G_q$ to obtain lower bounds on the extremal function ex(n;C₄), for some n < q² + q + 1. In particular, we construct a C₄-free graph on n = q² − √q vertices and 1/2q(q²−1) − 1/2√q(q − 1) edges, for a square prime power q.
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs -Matrices -Polarity -Size -Graph theory -Matrius (Matemàtica) -Grafs, Teoria de
Rights:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Published version Article
Share: