In this paper, we compute the Laplacian spectrum of non-commuting graphs of some classes of finite non-abelian groups. Our computations reveal that the non-commuting graphs of all the groups considered in this paper are L-integral. We also obtain some conditions on a group G so that its non-commuting graph is L-integral.

Some combinatorial and spectral properties of König-Egerváry (K-E) graphs are presented. In particular, some new combinatorial characterizations of K-E graphs are introduced, the Laplacian spectrum of particular families of K-E graphs is deduced, and a lower and upper bound on the largest and smallest adjacency eigenvalue, respectively, of a K-E graph are determined.

A dumbbell graph, denoted by Da,b,c, is a bicyclic graph consisting of two vertexdisjoint cycles Ca, Cb and a path Pc+3 (c > −1) joining them having only its end-vertices in common with the two cycles. In this paper, we study the spectral characterization w.r.t. the adjacency spectrum of Da,b,0 (without cycles C4) with gcd(a, b) > 3, and we complete the research started in [J.F. Wang et al., A ...

Abstract. Inspired by the graph Laplacian and the point integral method, we introduce a novel weighted graph Laplacian method to compute a smooth interpolation function on a point cloud in high dimensional space. The numerical results in semi-supervised learning and image inpainting show that the weighted graph Laplacian is a reliable and efficient interpolation method. In addition, it is easy ...

Abstract We show how the spectrum of a graph Laplacian changes with respect to certain type rank-one perturbation. apply our finding give new short proofs spectral version Kirchhoff’s Matrix Tree Theorem and known derivations for characteristic polynomials Laplacians several well-known families graphs, including complete, complete multipartite, crown threshold graphs.

Exploring common features and universal qualities shared by a particular class of networks in biological and other domains is one of the important aspects of evolutionary study. In an evolving system, evolutionary mechanism can cause functional changes that forces the system to adapt to new configurations of interaction pattern between the components of that system (e.g. gene duplication and mu...

Taking a Fiedler’s result [1] on the spectrum of a matrix formed from two symmetric matrices as a motivation, a more general result is deduced and applied to the determination of adjacency and Laplacian spectra of graphs obtained by a generalized join graph operation on families of graphs (regular in the case of adjacency spectra and arbitrary in the case of Laplacian spectra). Some additional ...

Let Pn be a pentagonal chain with 2n pentagons in which two edges common can regarded as adding one vertex and to hexagon. Thus, the linear derivation chains QPn represent graph obtained by attaching four-membered rings every of Pn. In this article, Laplacian spectrum consisting eigenvalues symmetric matrices is determined. Next, formulas for invariants that represented spectrum, namely, Kirchh...

If G is a graph, its Laplacian is the difference of the diagonal matrix of its vertex degrees and its adjacency matrix. The main thrust of the present article is to prove several Laplacian eigenvector “principles” which in certain cases can be used to deduce the effect on the spectrum of contracting, adding or deleting edges and/or of coalescing vertices. One application is the construction of ...