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• W3011460043 abstract "Given a simple connected graph G, let D ( G ) be the distance matrix, D L ( G ) be the distance Laplacian matrix, D Q ( G ) be the distance signless Laplacian matrix, and T r ( G ) be the vertex transmission diagonal matrix of G. We introduce the generalized distance matrix D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where α ∈ [ 0 , 1 ] . Noting that D 0 ( G ) = D ( G ) , 2 D 1 2 ( G ) = D Q ( G ) , D 1 ( G ) = T r ( G ) and D α ( G ) − D β ( G ) = ( α − β ) D L ( G ) , we reveal that a generalized distance matrix ideally bridges the spectral theories of the three constituent matrices. In this paper, we obtain some sharp upper and lower bounds for the generalized distance energy of a graph G involving different graph invariants. As an application of our results, we will be able to improve some of the recently given bounds in the literature for distance energy and distance signless Laplacian energy of graphs. The extremal graphs of the corresponding bounds are also characterized." @default.
• W3011460043 created "2020-03-23" @default.
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• W3011460043 date "2020-03-16" @default.
• W3011460043 modified "2023-09-27" @default.
• W3011460043 title "Sharp Bounds on (Generalized) Distance Energy of Graphs" @default.
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• W3011460043 doi "https://doi.org/10.3390/math8030426" @default.
• W3011460043 hasPublicationYear "2020" @default.
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