On Sum-Connectivity Matrix and Sum-Connectivity Energy of (Molecular) Graphs

If G is a (molecular) graph with n vertices, and di is the degree of its i-th vertex, then the sum-connectivity matrix of G is the n × n matrix whose (i, j) -entry is equal to 1/√di + dj if the i-th and the j-th vertices are adjacent and 0 otherwise. The sum-connectivity energy of a graph G is defined as the sum of the absolute values of the eigenvalues of the sumconnectivity matrix. Some properties including upper and lower bounds for the eigenvalues of the sum-connectivity matrix and the sum-connectivity energy are established, and the extremal cases are characterized.