Abstract
AbstractLet G = (V, E) be a connected graph, where V = {v1, v2, …, vn}. Let di denote the degree of vertex vi. The ABC matrix of G is defined as M(G) = (mij)n × n, where if vivj ∈ E, and 0 otherwise. The ABC spectral radius of G is the largest eigenvalue of M(G). In the present paper, two graph perturbations with respect to ABC spectral radius are established. By applying these perturbations, the trees with the third, fourth, and fifth largest ABC spectral radii are determined.
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