Geodesic
On the D α spectral radius of strongly connected digraphs
Filomat, Tome 35 (2021) no. 4, p. 1289

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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 α ∈ [0, 1], define the matrix D α (G) as D α (G) = αTr(G) + (1 − α)D(G). The D α spectral radius of G is the spectral radius of D α (G). In this paper, we first give some upper and lower bounds for the D α 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 α spectral radius. Finally, we obtain the D α eigenvalues of the join of certain regular digraphs
DOI : 10.2298/FIL2104289X
Classification : 05C50, 15A18
Keywords: strongly connected digraph, Dα spectral radius, bounds 
Weige Xi. On the D α spectral radius of strongly connected digraphs. Filomat, Tome 35 (2021) no. 4, p. 1289 . doi: 10.2298/FIL2104289X
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     author = {Weige Xi},
     title = {On the {D} \ensuremath{\alpha} spectral radius of strongly connected digraphs},
     journal = {Filomat},
     pages = {1289 },
     year = {2021},
     volume = {35},
     number = {4},
     doi = {10.2298/FIL2104289X},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2104289X/}
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