LAUSR

Spectral graph theory plays an important role in engineering. LetG be a simple graph of order nwith vertex setV � v1, v2, . . . , vn ???? ????. For vi ∈ V, the degree of the vertex vi, denoted by di, is the number of the vertices adjacent to vi. )e arithmetic-geometric adjacencymatrixAag(G) ofG is defined as the n × n matrix whose (i, j) entry is equal to ((di + dj)/2 ���� didj ???? ) if the vertices vi and vj are adjacent and 0 otherwise. )e arithmetic-geometric spectral radius and arithmetic-geometric energy of G are the spectral radius and energy of its arithmetic-geometric adjacencymatrix, respectively. In this paper, some new upper bounds on arithmeticgeometric energy are obtained. In addition, we present the Nordhaus–Gaddum-type relations for arithmetic-geometric spectral radius and arithmetic-geometric energy and characterize corresponding extremal graphs.