We study the transition matrix of a quantum walk on strongly regular graphs. It is proposed by Emms, Hancock, Severini and Wilson in 2006, that the spectrum of S+(U3), a matrix based on the amplitudes of walks in the quantum walk, distinguishes strongly regular graphs. We probabilistically compute the spectrum of the line intersection graphs of two non-isomorphic generalized quadrangles of orde...

In this paper, using matrix techniques, we compute the Ihara-zeta function and number of spanning trees join two semi-regular bipartite graphs. Furthermore, show that spectrum graphs can determine each other.

We characterize the distance-regular Ivanov–Ivanov–Faradjev graph from the spectrum, and construct cospectral graphs of the Johnson graphs, Doubled Odd graphs, Grassmann graphs, Doubled Grassmann graphs, antipodal covers of complete bipartite graphs, and many of the Taylor graphs. We survey the known results on cospectral graphs of the Hamming graphs, and of all distance-regular graphs on at mo...

The distance eigenvalues of a connected graph G are the eigenvalues of its distance matrix D, and they form the distance spectrum of G. A graph is called distance integral if its distance spectrum consists entirely of integers. We show that no nontrivial tree can be distance integral. We characterize distance integral graphs in the classes of graphs similar to complete split graphs, which, toge...

Expanding parameters of graphs (magnification constant, edge and vertex cutset expansion) are related by very simple inequalities to forwarding parameters (edge and vertex forwarding indices). This shows that certain graphs have eccentricity close to the diameter. Connections between the forwarding indices and algebraic parameters like the smallest eigenvalue of the Laplacian or the genus of th...

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.