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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.

Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy