The adjacency matrix of a non-oriented connected graph is symmetric, hence its spectrum is real. If the graph is bipartite, then the spectrum of its adjacency matrix is symmetric about 0. A few ...
Let $L$ be the discrete Laplacian associated to an undirected graph. It is well-known that the spectral gap of $L$, i.e. the smallest nonzero eigenvalue, is a measure of how well connected the graph ...
It is well-known that a random graph a.e. has diameter 2. It is also well-known that the number of distinct eigenvalues of a graph is at least the diameter plus one. But what is known about the ...