Nonexistence of Graphs with Cyclic Defect

Abstract

In this note we consider graphs of maximum degree $\Delta$, diameter $D$ and order ${\rm M}(\Delta,D) - 2$, where ${\rm M}(\Delta,D)$ is the Moore bound, that is, graphs of defect 2. Delorme and Pineda-Villavicencio conjectured that such graphs do not exist for $D\geq 3$ if they have the so called 'cyclic defect'. Here we prove that this conjecture holds.