Claw-free strictly Deza graphs

V. V. Kabanov ; A. V. Mityanina

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 367-387

Résumé

A Deza graph with parameters $(v,k,b,a)$ is a $k$-regular graph, which has exactly $v$ vertices and any two distinct vertices have either $a$ or $b$ common neighbors. A strictly Deza graph is a Deza graph of diameter $2$ that is not strongly regular. A claw-free graph is a graph in which no induced subgraph is a complete bipartite graph $K_{1,3}$. We proved if graph $G$ is a claw-free strictly Deza graph which contains a $3$-coclique then $G$ is either an $4 \times n$-lattice, where $n > 2$, $n \neq 4$, or the $2$-extension of the $3 \times 3$-lattice, or two strictly Deza graphs with the parameters $(9,4,2,1)$, or two strictly Deza graphs with the parameters $(12,6,3,2)$, or a Deza line graph with the parameters $(20,6,2,1)$.

Détail

Keywords: strictly Deza graphs, claw-free graphs.