On the spectral radius and the genus of graphs
Let \(G\) be a graph of genus \(g\) and let \(r(G)\) be the largest eigenvalue of the adjacency matrix of \(G\). The author proves that \(r(G)\leq(6| V(G)|+12g-6)^{1/2}\). The bound is slightly improved in the case of some small genus surfaces.
scientific article; zbMATH DE number 839124