In this paper, some new properties are presented to the extremal graphs with largest (signless Laplacian) spectral radii in the set of all the connected graphs with prescribed degree sequences, via which we determine all the extremal tricyclic graphs in the class of connected tricyclic graphs with prescribed degree sequences, and we also prove some majorization theorems of tricyclic graphs with...

Let S(n, c) = K1∨(cK2∪(n−2c−1)K1), where n ≥ 2c+1 and c ≥ 0. In this paper, S(n, c) and its complement are shown to be determined by their Laplacian spectra, respectively. Moreover, we also prove that S(n, c) and its complement are determined by their signless Laplacian spectra, respectively.

In this paper we define extended corona and extended neighborhood corona of two graphs G1 and G2, which are denoted by G1 • G2 and G1 ∗ G2 respectively. We compute their adjacency spectrum, Laplacian spectrum and signless Laplacian spectrum. As applications, we give methods to construct infinite families of integral graphs, Laplacian integral graphs and expander graphs from known ones.

The spectrum of the Laplacian, signless Laplacian and adjacency matrices of the family of the weighted graphs R{H}, obtained from a connected weighted graph R on r vertices and r copies of a modified Bethe tree H by identifying the root of the i-th copy of H with the i-th vertex of R, is determined.

In this paper, we give some new sharp upper and lower bounds for the spectral radius of a nonnegative irreducible matrix. Using these bounds, we obtain some new and improved bounds for the signless Laplacian spectral radius of a graph or a digraph.

Let S(n, c) = K1∨(cK2∪(n−2c−1)K1), where n ≥ 2c+1 and c ≥ 0. In this paper, S(n, c) and its complement are shown to be determined by their Laplacian spectra, respectively. Moreover, we also prove that S(n, c) and its complement are determined by their signless Laplacian spectra, respectively.

In a graph, a matching cut is an edge cut that is a matching. Matching Cut is the problem of deciding whether or not a given graph has a matching cut, which is known to be NP-complete even when restricted to bipartite graphs. It has been proved that Matching Cut is polynomially solvable for graphs of diameter two. In this paper, we show that, for any fixed integer d ≥ 4, Matching Cut is NP-comp...

In a weighted undirected graph, a matching is said to be α-robust if for all p, the total weight of its heaviest p edges is at least α times the maximum weight of a p-matching in the graph. Here a p-matching is a matching with at most p edges. In 2002, Hassin and Rubinstein [5] showed that every graph has a 1 √ 2 -robust matching and it can be found by k-th power algorithm in polynomial time. I...

Authors propose several approaches for increasing performance of multiplicative inversion algorithm in binary fields based on Extended Euclidean Algorithm (EEA). First approach is based on Extended Euclidean Algorithm specificity: either invariant polynomial v remains intact or swaps with invariant polynomial u . It makes it possible to avoid necessity of polynomial v degree computing. The seco...