Several researchers have recently explored various graph parameters that can or cannot be characterized by the spectrum of a matrix associated with graph. In this paper, we show several NP-hard zero forcing numbers are not spectra types matrices particular, consider standard forcing, positive semidefinite and skew provide constructions infinite families pairs cospectral graphs, which different ...

A new generalization of Fiedler's lemma is obtained by introducing the concept main function a matrix. As applications, universal spectra H-join any graphs (possibly non-regular) and adjacency H-generalized join constrained (arbitrary) vertex subsets are obtained. The generalized corona deduced from graphs. Also, construction infinitely many pairs non-regular cospectral provided.

A new proof concerning the determinant of the adjacency matrix of the line graph of a tree is presented and an invariant for line graphs, introduced by Cvetković and Lepović, with least eigenvalue at least −2 is revisited and given a new equivalent definition [D. Cvetković and M. Lepović. Cospectral graphs with least eigenvalue at least −2. Publ. Inst. Math., Nouv. Sér., 78(92):51–63, 2005.]. E...

A new proof concerning the determinant of the adjacency matrix of the line graph of a tree is presented and an invariant for line graphs, introduced by Cvetković and Lepović, with least eigenvalue at least −2 is revisited and given a new equivalent definition [D. Cvetković and M. Lepović. Cospectral graphs with least eigenvalue at least −2. Publ. Inst. Math., Nouv. Sér., 78(92):51–63, 2005.]. E...

Let G be a graph of order n, A(G) its adjacency matrix and D(G) the diagonal degrees G. In 2017, for every α in [0, 1], Nikiforov defined Aα(G) = αD(G) + (1 − α)A(G). this paper, we investigate Aα-spectrum graphs obtained from duplicate corona operations. As an application our results, provide conditions construction some pairs non isomorphic Aα-cospectral graphs.

The k-th power of a n-vertex graph X is the iterated cartesian product of X with itself. The k-th symmetric power of X is the quotient graph of certain subgraph of its k-th power by the natural action of the symmetric group. It is natural to ask if the spectrum of the k-th power –or the spectrum of the k-th symmetric power– is a complete graph invariant for small values of k, for example, for k...

Let Γ = (G,σ) be a signed graph, where σ is the sign function on edges of G. In this paper, we use operation partial transpose to obtain non-isomorphic Laplacian cospectral graphs. We will introduce two new operations These establish relationship between adjacency spectrum one graph with another graph. As an application, these utilized construct several pairs Finally, integral