Covering spaces of locally homogeneous graphs (Q1309469)

A graph \(G\) is said to be locally \(L\) if for each vertex \(v\) of \(G\), the induced subgraph on the neighbors of \(v\) is isomorphic to the graph \(L\). Following \textit{M. A. Ronan} [Q. J. Math., Oxf. II. Ser. 32, 225-233 (1981; Zbl 0466.57004)] and \textit{A. Vince} [J. Graph Theory 5, 417-422 (1981; Zbl 0472.05055)], topological methods are used for deriving several results about existence of locally \(L\) graphs. For example, if \(L\) is a graph such that \(| E(L)| \leq 3 | V(L)|/2-3\) and if there is a locally \(L\) graph \(G\) of order \(n\), then one can find connected locally \(L\) graphs of order \(kn\) for any positive integer \(k\).