Locally Shrikhande graphs and their automorphisms
A graph on the vertex set \(X\times Y\) is an \(m\times n\)-graph provided that \((x_1,y_1)\) is adjacent to \((x_2,y_2)\) if and only if \(x_1=x_2\) or \(y_1=y_2\). An \(m\times m\)-graph, called lattice graph, is strongly regular with parameters \(v=m^2\), \(k=2m-2\), \(\lambda=m-2\). A strongly regular graph with parameters \((16,6,2,2)\) is called a Shrikhande graph. The main result consists in describing locally Shrikhande graphs, i.e. graphs all whose neighborhoods of vertices are Shrikhande graphs. (Similar results for locally lattice graphs are already known.) Namely, it is shown that every connected locally Shrikhande graph has either 80 or 40 vertices, and its possible diagrams are represented.
scientific article; zbMATH DE number 1286306