TY - JOUR

T1 - Some upper and lower bounds for Dα-energy of graphs

AU - Alhevaz, Abdollah

AU - Baghipur, Maryam

AU - Hashemi, Ebrahim

AU - Shang, Yilun

N1 - Funding information: The authors would like to thank the anonymous referee(s) and the Editor for their valuable comments to improve the presentation of the manuscript. Y. Shang was supported in part by the UoA Flexible Fund No. 201920A1001 from Northumbria University.

PY - 2023/5/10

Y1 - 2023/5/10

N2 - The generalized distance matrix of a connected graph G, denoted by Dα(G), is defined as (formula presented). Here, D(G) is the distance matrix and T r(G) represents the vertex transmissions. Let (formula presented) be the eigenvalues of Dα(G) and let W (G) be the n∑ Wiener index. The generalized distance energy of G can be defined as (formula presented) In this paper, we develop some new theory regarding the generalized distance energy EDα (G) for a connected graph G. We obtain some sharp upper and lower bounds for EDα (G) connecting a wide range of parameters in graph theory including the maximum degree ∆, the Wiener index W (G), the diameter d, the transmission degrees, and the generalized distance spectral spread DαS(G). We characterized the special graph classes that attain the bounds. i=1.

AB - The generalized distance matrix of a connected graph G, denoted by Dα(G), is defined as (formula presented). Here, D(G) is the distance matrix and T r(G) represents the vertex transmissions. Let (formula presented) be the eigenvalues of Dα(G) and let W (G) be the n∑ Wiener index. The generalized distance energy of G can be defined as (formula presented) In this paper, we develop some new theory regarding the generalized distance energy EDα (G) for a connected graph G. We obtain some sharp upper and lower bounds for EDα (G) connecting a wide range of parameters in graph theory including the maximum degree ∆, the Wiener index W (G), the diameter d, the transmission degrees, and the generalized distance spectral spread DαS(G). We characterized the special graph classes that attain the bounds. i=1.

KW - Distance (signless Laplacian) matrix

KW - Generalized distance energy

KW - Generalized distance matrix

KW - Generalized distance spectral spread

KW - Transmission regular graph

UR - http://www.scopus.com/inward/record.url?scp=85160093302&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85160093302

SN - 2148-838X

VL - 10

SP - 73

EP - 86

JO - Journal of Algebra Combinatorics Discrete Structures and Applications

JF - Journal of Algebra Combinatorics Discrete Structures and Applications

IS - 2

ER -