Abstract
Let [Formula: see text] be a simple graph of order [Formula: see text] with vertex set [Formula: see text] and edge set [Formula: see text]. The arithmetic–geometric matrix [Formula: see text] of [Formula: see text] is a matrix of order [Formula: see text] defined by [Formula: see text] if [Formula: see text] and 0 otherwise, where [Formula: see text] stands for the degree of the vertex [Formula: see text] in [Formula: see text]. The arithmetic–geometric characteristic polynomial of [Formula: see text] is the characteristic polynomial of [Formula: see text]. The arithmetic–geometric energy [Formula: see text] of [Formula: see text] is the sum of absolute values of all eigenvalues of [Formula: see text]. In this paper, we obtain the arithmetic–geometric characteristic polynomial and arithmetic–geometric energy of some specific graphs. In addition, we also consider the arithmetic–geometric characteristic polynomial and arithmetic–geometric energy change of these graphs when one edge is deleted.
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