Harishchandra S. Ramane, Mahadevappa M. Gundloor, Sunilkumar M. Hosamani, Seidel Equienergetic Graphs, BMSA Volume 16, Bulletin of Mathematical Sciences and Applications (Volume 16)
https://www.scipress.com/BMSA.16.62
Abstract:
    The Seidel matrix <i>S</i>(<i>G</i>) of a graph <i>G</i> is the square matrix with diagonal entries zeroes and off diagonal entries are – 1 or 1 corresponding to the adjacency and non-adjacency. The Seidel energy <i>SE</i>(<i>G</i>) of <i>G</i> is defined as the sum of the absolute values of the eigenvalues of <i>S</i>(<i>G</i>). Two graphs <i>G</i><sub>1</sub> and <i>G</i><sub>2</sub> are said to be Seidel equienergetic if <i>SE</i>(<i>G</i><sub>1</sub>) = <i>SE</i>(<i>G</i><sub>2</sub>). We establish an expression for the characteristic polynomial of the Seidel matrix and for the Seidel energy of the join of regular graphs. Thereby construct Seidel non cospectral, Seidel equienergetic graphs on <i>n</i> vertices, for all <i>n</i> ≥ 12
Keywords:
    Join of Graphs, Seidel Eigenvalues, Seidel Energy