On the Spectral Parameters of Certain Cartesian Products of Graphs with $$P_2$$

Abstract

A structure descriptor that is largely studied in the context of spectral graph theory is the energy of a graph. It is defined as the sum of the absolute values of the eigenvalues of the adjacency matrix of the graph. Spectral Graph Theory is the study of properties of graphs and the matrices associated with them such as its adjacency matrix or Laplacian matrix. It has enormous applications in diverse areas such as chemistry, coding theory, information theory, geographic studies, etc. In this paper, we have obtained the values of energy, spectral radius, second-largest eigenvalue, least eigenvalue, spread and separator of book graph, ladder graph and prism graph and supplement our results using the MATLAB programs.