Smith graph (original) (raw)

In the mathematical field of graph theory, a Smith graph is either of two kinds of graph. * It is a graph whose adjacency matrix has largest eigenvalue at most 2, or has spectral radius 2 or at most 2. The graphs with spectral radius 2 form two infinite families and three sporadic examples; if we ask for spectral radius at most 2 then there are two additional infinite families and three more sporadic examples. The infinite families with spectral radius less than 2 are the paths and the paths with one extra edge attached to the vertex next to an endpoint; the infinite families with spectral radius exactly 2 are the cycles and the paths with an extra edge attached to the each of the vertices next to an endpoint.