ABC Spectral Radius

The ABC (atom-bond connectivity) spectral radius rho_(ABC) of a graph is defined as the largest eigenvalue of its ABC matrix.

Chen (2019) showed that for a tree on 3 or more vertices,


where the lower bound corresponds to the ABC spectral radius of the path graph P_n and the upper to that of the star graph S_n (Zheng et al. 2023).

See also

ABC Matrix, Graph Eigenvalue, Spectral Radius

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Chen, X. "On Extremality of ABC Spectral Radius of a Tree." Linear Algebra Appl. 564, 159-169, 2019.Estrada, E. "The ABC Matrix." J. Math. Chem. 55, 1021-1033, 2017.Zheng, R.; Su, P.; and Jin. S. "Arithmetic-Geometric Matrix of Graphs and Its Applications." Appl. Math. Comput. 42, 127764, 1-11, 2023.

Cite this as:

Weisstein, Eric W. "ABC Spectral Radius." From MathWorld--A Wolfram Web Resource.

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