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.

Recall that, given a graph G, the matrix Q = D + A is called the signless Laplacian, where A is the adjacency matrix and D is the diagonal matrix of vertex degrees. The matrix L = D − A is known as the Laplacian of G. Graphs with the same spectrum of an associated matrix M are called cospectral graphs with respect to M , or M–cospectral graphs. A graph H cospectral with a graph G, but not isomo...

Let n be any positive integer and Fn be the friendship (or Dutch windmill) graph with 2n+1 vertices and 3n edges. Here we study graphs with the same adjacency spectrum as Fn. Two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. Let G be a graph cospectral with Fn. Here we prove that if G has no cycle of length 4 or 5, then G ∼= Fn. Moreover if G...

We introduce a generalized adjacency matrix in order to distinguish cospectral graphs. Our reasoning is motivated by the work of Johnson and Newman properties p-adic numbers. Using polynomial time algorithm, we comment on computer experiments with which can (non-isomorphic)

The distance matrix of a connected graph is the symmetric matrix with columns and rows indexed by the vertices and entries that are the pairwise distances between the corresponding vertices. We give a construction for graphs which differ in their edge counts yet are cospectral with respect to the distance matrix. Further, we identify a subgraph switching behavior which constructs additional dis...

The symmetric m-th power of a graph is the graph whose vertices are m-subsets of vertices and in which two m-subsets are adjacent if and only if their symmetric difference is an edge of the original graph. It was conjectured that there exists a fixed m such that any two graphs are isomorphic if and only if their m-th symmetric powers are cospectral. In this paper we show that given a positive i...