Nonexistence of graphs with cyclic defect

In this note we consider graphs of maximum degree ∆, diameter D and order M(∆, D) − 2, where M(∆, D) is the Moore bound, that is, graphs of defect 2. In [1] Delorme and Pineda-Villavicencio conjectured that such graphs do not exist for D ≥ 3 if they have the so called 'cyclic defect'. Here we prove that this conjecture holds.