Non-existence of bipartite graphs of diameter at least \(4\) and defect \(2\)
This paper proves a conjecture by settling the non-existence of bipartite \((\Delta,D,-2)\) graphs for all \(\Delta \geq 3\) and all \(D \geq 6\), using the reasoning in the proofs of the non-existence of Moore graphs for \(\Delta\geq 3\) and \(D\geq 3\) and the non-existence of regular graphs of degree \(\Delta\geq 3\), even girth \(g\geq 2\) and order \(M^b_{\Delta,g/2}+2\) and the non-existence of regular graphs of \(\Delta\geq 3\) odd girth \(g\geq 5\) and order \(M_{\Delta,(g-1)/2}+1\).
Moore bipartite graphs, Dickson polynomials of the second kind
scientific article; zbMATH DE number 5968633
scientific article