Let A(G) and D(G) be the adjacency matrix and the degree matrix of a graph G, respectively. For any real α [0, 1], we consider Aα (G) = αD(G) + (1-α)A(G) as a graph matrix, whose largest eigenvalue is called the Aα-spectral radius of G. We first show that the smallest limit point for the Aα-spectral radius of graphs is 2, and then we characterize the connected graphs whose Aα-spectral radius is at most 2. Finally, we show that all such graphs, with four exceptions, are determined by their Aα-spectra.
Graphs Whose Aα-Spectral Radius Does Not Exceed 2 / Wang, J. F.; Wang, J.; Liu, X.; Belardo, F.. - In: DISCUSSIONES MATHEMATICAE. GRAPH THEORY. - ISSN 1234-3099. - 40:2(2020), pp. 677-690. [10.7151/dmgt.2288]
Graphs Whose Aα-Spectral Radius Does Not Exceed 2
Belardo F.
2020
Abstract
Let A(G) and D(G) be the adjacency matrix and the degree matrix of a graph G, respectively. For any real α [0, 1], we consider Aα (G) = αD(G) + (1-α)A(G) as a graph matrix, whose largest eigenvalue is called the Aα-spectral radius of G. We first show that the smallest limit point for the Aα-spectral radius of graphs is 2, and then we characterize the connected graphs whose Aα-spectral radius is at most 2. Finally, we show that all such graphs, with four exceptions, are determined by their Aα-spectra.| File | Dimensione | Formato | |
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