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

Autor
Abreu, M.; Balbuena, C.; Labbate, D.
Tipus d'activitat
Article en revista
Revista
Designs codes and cryptography
Data de publicació
2010
Volum
55
Número
2-3
Pàgina inicial
221
Pàgina final
233
DOI
https://doi.org/10.1007/s10623-010-9364-1 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/8737 Obrir en finestra nova
URL
http://www.springerlink.com/content/0643j32v62708350/fulltext.pdf Obrir en finestra nova
Resum
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,...
Citació
Abreu, M.; Balbuena, C.; Labbate, D. Adjacency matrices of polarity graphs and of other C4-free graphs of large size. "Designs codes and cryptography", 2010, vol. 55, núm. 2-3, p. 221-233.
Grup de recerca
COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions

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