Nonexistence of graphs with cyclic defect (Q540060)

Summary: We consider graphs of maximum degree \(\Delta \), diameter \(D\) and order \(M(\Delta , D) - 2\), where \(M(\Delta, D)\) is the Moore bound, that is, graphs of defect 2. \textit{C. Delorme} and \textit{G. Pineda-Villavicencio} [``On graphs with cyclic defect or excess,'' Electron. J. Comb. 17, No.\,1, Research Paper P143, 25 p., electronic only (2010; Zbl 1204.05043)] 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.