NEW RESULTS ON α-SPECTRAL RADIUS OF GRAPHS

作者：Lin, Hongying; Zhou, Bo^*

来源：Operators and Matrices, 2021, 15(2): 435-450.

DOI：10.7153/oam-2021-15-30

• alpha-spectral radius
• alpha-Perron vector
• graph
• odd vertices
• maximum degree

For 0 <= alpha < 1, Nikiforov proposed to study the spectral properties of the family of matrices A(alpha) (G) = alpha D( G)+(1-alpha) A(G) of a graph G, where D(G) is the degree diagonal matrix and A(G) is the adjacency matrix. The alpha-spectral radius of G is the largest eigenvalue of A(alpha)(G). For 0 <= alpha < 1, we give a lower bound for the alpha-spectral radius, and bounds for the maximum and minimum entries of the alpha-Perron vector, and we determine the unique graph with maximum a -spectral radius among graphs with given number of odd vertices.