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The spectral radius of a uniform hypergraph is defined to be that of the adjacency tensor of the hypergraph. It is known that the unique unicyclic hypergraph with the largest spectral radius is a nonlinear hypergraph, and the unique linear unicyclic hypergraph with the largest spectral radius is a power hypergraph. In this paper we determine the unique linear unicyclic hypergraph with the second or third largest spectral radius, where the former hypergraph is a power hypergraph and the latter hypergraph is a non-power hypergraph. [ABSTRACT FROM AUTHOR]

Using the Poisson formula for resultants, and variants of the chip-firing game on graphs, we provide a combinatorial method for computing a class of resultants corresponding to the characteristic polynomials of the adjacency tensors of starlike hypergraphs including hyperpaths and hyperstars, which are given recursively and explicitly. [ABSTRACT FROM AUTHOR]

We investigate how the algebraic connectivity of a graph changes by relocating a connected branch from one vertex to another vertex, and then minimize the algebraic connectivity among all connected graphs of order n with fixed domination number γ≤n+23, and finally present a lower bound for the algebraic connectivity in terms of the domination number. We also characterize the minimum algebraic connectivity of graphs with domination number half their order. [ABSTRACT FROM AUTHOR]

Let $$\fancyscript{B}(n,r)$$ be the set of all bicyclic graphs with $$n$$ vertices and $$r$$ cut edges. In this paper we determine the unique graph with maximal adjacency spectral radius or signless Laplacian spectral radius among all graphs in $$\fancyscript{B}(n,r)$$ . [ABSTRACT FROM AUTHOR]

Let G be a simple graph and let Q ( G) be the signless Laplacian matrix of G. In this paper we obtain some results on the spectral perturbation of the matrix Q ( G) under an edge addition or an edge contraction. [ABSTRACT FROM AUTHOR]

In this paper we characterize the unique graph whose least eigenvalue attains the minimum among all connected graphs of fixed order and given number of cut edges. [ABSTRACT FROM AUTHOR]

In [6], Guo and Tan have shown that 2 is a Laplacian eigenvalue of any tree with perfect matchings. For trees without perfect matchings, we study whether 2 is one of its Laplacian eigenvalues. If the matching number is 1 or 2, the answer is negative; otherwise, there exists a tree with that matching number which has (has not) the eigenvalue 2. In particular, we determine all trees with matching number 3 which has the eigenvalue 2. [ABSTRACT FROM AUTHOR]