In this paper, we define duplication corona, duplication neighborhood corona and duplication edge corona of two graphs. We compute their adjacency spectrum, Laplacian spectrum and signless Laplacian. As an application, our results enable us to construct infinitely many pairs of cospectral graphs and also integral graphs.

We address the study of controllability of a closed quantum system whose dynamical Lie algebra is generated by adjacency matrices of graphs. We characterize a large family of graphs that renders a system controllable. The key property is a novel graph-theoretic feature consisting of a particularly disordered cycle structure. Disregarding efficiency of control functions, but choosing subfamilies...

We give several old and some new applications of eigenvalue interlacing to matrices associated to graphs. Bounds are obtained for characteristic numbers of graphs, such as the size of a maximal (colclique, the chromatic number, the diameter, and the bandwidth, in terms of the eigenvalues of the Standard adjacency matrix or the Laplacian matrix. We also deal with inequalities and regularity resu...

The energy of signed graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Two signed graphs are said to be equienergetic if they have same energy. In the literature the construction of equienergetic signed graphs are reported. In this paper we obtain the characteristic polynomial and energy of the join of two signed graphs and thereby we give another construction ...

This is an expository survey of the uses of matrices in the theory of simple graphs with signed edges. A signed simple graph is a graph, without loops or parallel edges, in which every edge has been declared positive or negative. For many purposes the most significant thing about a signed graph is not the actual edge signs, but the sign of each circle (or ‘cycle’ or ’circuit’), which is the pro...

We consider three models of sparse random graphs: undirected and directed Erdős–Rényi graphs bipartite graph with two equal parts. For such graphs, we show that if the edge connectivity probability p satisfies $$np\ge \log n+k(n)$$ $$k(n)\rightarrow \infty $$ as $$n\rightarrow , then adjacency matrix is invertible approaching one (n number vertices in former cases same for each part latter case...

In this paper, we address the scalability issue plaguing graph-based semi-supervised learning via a small number of anchor points which adequately cover the entire point cloud. Critically, these anchor points enable nonparametric regression that predicts the label for each data point as a locally weighted average of the labels on anchor points. Because conventional graph construction is ineffic...

We explore algebraic and spectral properties of weighted graphs containing twin vertices that are useful in quantum state transfer. extend the notion adjacency strong cospectrality to Hermitian matrices, with focus on generalized matrix normalized matrix. then determine necessary sufficient conditions such a pair graph exhibits respect above-mentioned matrices. also when is preserved under Cart...

Graphs can be used in applied in both an unsupervised and supervised context that can augment classification tasks. This paper focuses on a set of movie graphs that correspond to actor interactions in movies associated with various genres. I first compare the graph statistics between two disparate genres and perform random walks and analyze the eigenvalue and eigenvectors of the adjacency matri...

A mixed graph means a graph containing both oriented edges and undirected edges. The nullity of the Hermitian-adjacency matrix of a mixed graph G, denoted by ηH(G), is referred to as the multiplicity of the eigenvalue zero. In this paper, for a mixed unicyclic graph G with given order and matching number, we give a formula on ηH(G), which combines the cases of undirected and oriented unicyclic ...