On the Generalized Distance Energy of Graphs

Abdollah Alhevaz, Maryam Baghipur, Hilal Ahmad Ganie, Yilun Shang

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)
24 Downloads (Pure)


The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 - α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.
Original languageEnglish
Article number7
Issue number1
Publication statusPublished - 19 Dec 2019


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