The time fractional diffusion equation with appropriate initial and boundary conditions in an n-dimensional whole-space and half-space is considered. Its solution has been obtained in terms of Green functions by Schneider and Wyss. For the problem in whole-space, an explicit representation of the Green functions can also be obtained. However, an explicit… (More)
Two graphs G and H are called R-cospectral if A(G)+yJ and A(H)+yJ (where A(G), A(H) are the adjacency matrices of G and H, respectively, J is the all-one matrix) have the same spectrum for all y ∈ R. In this note, we give a necessary condition for having R-cospectral graphs. Further, we provide a sufficient condition ensuring only irrational orthogonal… (More)
In this note, we consider connected graphs with exactly two main eigenvalues. We will give several constructions for them, and as a consequence we show a family of those graphs with an unbounded number of distinct va-lencies.
The †-shape tree is the coalescence of the star K 1,4 and the path P n−4 with respect to two pendent vertices. In this paper, it is showed that the †-shape tree is determined by its adjacency spectrum if and only if n = 2k + 9 (k = 0, 1,. . .). Furthermore, all the cospectral mates of the †-shape tree are found when n = 2k + 9.