General Zagreb Adjacency Matrix

Let A ( G ) and D ( G ) be the adjacency matrix and the degree diagonal matrix of a graph G , respectively. For any real number α , the general Zagreb adjacency matrix of G is defined as Z α ( G ) = D α ( G )+ A ( G ) . In this paper, the positive semidefiniteness, spectral moment, coefficients of characteristic polynomials, and energy of the general Zagreb adjacency matrix are studied. The obtained results extend the corresponding results concerning the signless Laplacian matrix, the vertex Zagreb adjacency matrix, and the forgotten adjacency matrix.