Authors: Crevel Bautista-Santiago ¹; Javier Cano ²; Ruy Fabila-Monroy ³; David Flores-Peñaloza ⁴; Hernàn González-Aguilar ⁵; Dolores Lara ⁶; Eliseo Sarmiento ⁷; Jorge Urrutia ²

• 1 Division de Ciencas Basicas e Ingeniera [Azcapotzalco]
• 2 Instituto de Matematicas [México]
• 3 Centro de Investigacion y de Estudios Avanzados del Instituto Politécnico Nacional
• 4 Departamento de Matematicas [Mexico]
• 5 Facultad de Ciencas [Mexico]
• 6 Departament de Matemàtica Aplicada II
• 7 Escuela Superior de Fisica y Matematicas [Mexico]

Let P be a set of n points in general position in the plane. A subset I of P is called an island if there exists a convex set C such that I = P \C. In this paper we define the generalized island Johnson graph of P as the graph whose vertex consists of all islands of P of cardinality k, two of which are adjacent if their intersection consists of exactly l elements. We show that for large enough values of n, this graph is connected, and give upper and lower bounds on its diameter.