Some upper and lower bounds for Dα-energy of graphs

Abdollah Alhevaz; Maryam Baghipur; Ebrahim Hashemi; Yilun Shang

Some upper and lower bounds for D_α-energy of graphs

Abdollah Alhevaz, Maryam Baghipur, Ebrahim Hashemi, Yilun Shang^*

^*Corresponding author for this work

Computer and Information Sciences Department

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

17 Downloads (Pure)

Abstract

The generalized distance matrix of a connected graph G, denoted by D_α(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 D_α(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 E^Dα (G) for a connected graph G. We obtain some sharp upper and lower bounds for E^Dα (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 D_αS(G). We characterized the special graph classes that attain the bounds. i=1.

Original language	English
Pages (from-to)	73-86
Number of pages	14
Journal	Journal of Algebra Combinatorics Discrete Structures and Applications
Volume	10
Issue number	2
Publication status	Published - 10 May 2023

Keywords

Distance (signless Laplacian) matrix
Generalized distance energy
Generalized distance matrix
Generalized distance spectral spread
Transmission regular graph

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Cite this

@article{3e57db6a8f68423189151aa174e705e1,

title = "Some upper and lower bounds for Dα-energy of graphs",

abstract = "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.",

keywords = "Distance (signless Laplacian) matrix, Generalized distance energy, Generalized distance matrix, Generalized distance spectral spread, Transmission regular graph",

author = "Abdollah Alhevaz and Maryam Baghipur and Ebrahim Hashemi and Yilun Shang",

note = "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.",

year = "2023",

month = may,

day = "10",

language = "English",

volume = "10",

pages = "73--86",

journal = "Journal of Algebra Combinatorics Discrete Structures and Applications",

issn = "2148-838X",

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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

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JO - Journal of Algebra Combinatorics Discrete Structures and Applications

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