Upper Bounds of the Spectral Radius of Graphs in Terms of Genus

LetGbe a simple graph withnvertices and orientable genusgand non-orientable genush. Letρ(G) be the spectral radius of the adjacency matrixAofG. We obtain the following sharp bounds ofρ(G): (1)ρ(G)⩽1+3n+12g−8; (2)ρ(G)⩽1+3n+6h−8.