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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)

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.

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.

Cubic graphs of given order with maximum number of triangles are characterized. Consequently, it is proved that certain cubic graphs with maximum number of triangles are determined by their adja-cency spectrum.

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