Open AccessOn the Dα spectral radius of strongly connected digraphs
Author(s) -
Weige Xi
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2104289x
Subject(s) - spectral radius , mathematics , digraph , combinatorics , vertex (graph theory) , eigenvalues and eigenvectors , radius , diagonal , upper and lower bounds , diagonal matrix , matrix (chemical analysis) , discrete mathematics , mathematical analysis , geometry , physics , graph , quantum mechanics , computer security , materials science , computer science , composite material
Let G be a strongly connected digraph with distance matrix D(G) and let Tr(G) be the diagonal matrix with vertex transmissions of G. For any real ? ? [0, 1], define the matrix D?(G) as D?(G) = ?Tr(G) + (1-?)D(G). The D? spectral radius of G is the spectral radius of D?(G). In this paper, we first give some upper and lower bounds for the D? spectral radius of G and characterize the extremal digraphs. Moreover, for digraphs that are not transmission regular, we give a lower bound on the difference between the maximum vertex transmission and the D? spectral radius. Finally, we obtain the D? eigenvalues of the join of certain regular digraphs.