A general formula is obtained for the characteristic polynomial of a graph modied by the addition of a vertex with any prescribed set of neighbours.
We discuss means of constructing fullerene graphs from their eigenvalues and angles. An algorithm for such a construction is given.
Let G be a connected graph whose least eigenvalue λ(G) is minimal among the connected graphs of prescribed order and size. We show first that either G is complete or λ(G) is a simple eigenvalue. In the latter case, the sign pattern of a corresponding eigenvector determines a partition of the vertex set, and we study the structure of G in terms of this… (More)