On maximal distance energy

Shaowei Sun; Kinkar Chandra Das; Yilun Shang

doi:10.3390/math9040360

On maximal distance energy

Shaowei Sun, Kinkar Chandra Das, Yilun Shang

Department of Mathematics

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

5 Scopus citations

Abstract

Let G be a graph of order n. If the maximal connected subgraph of G has no cut vertex then it is called a block. If each block of graph G is a clique then G is called clique tree. The distance energy E_D (G) of graph G is the sum of the absolute values of the eigenvalues of the distance matrix D(G). In this paper, we study the properties on the eigencomponents corresponding to the distance spectral radius of some special class of clique trees. Using this result we characterize a graph which gives the maximum distance spectral radius among all clique trees of order n with k cliques. From this result, we confirm a conjecture on the maximum distance energy, which was given in Lin et al. Linear Algebra Appl 467(2015) 29-39.

Original language	English
Article number	360
Pages (from-to)	1-7
Number of pages	7
Journal	Mathematics
Volume	9
Issue number	4
DOIs	https://doi.org/10.3390/math9040360
State	Published - 2 Feb 2021

Keywords

Distance energy
Distance matrix
Distance spectral radius

Access to Document

10.3390/math9040360

Cite this

@article{0a117638186e47408998cd5b5f7cd84e,

title = "On maximal distance energy",

abstract = "Let G be a graph of order n. If the maximal connected subgraph of G has no cut vertex then it is called a block. If each block of graph G is a clique then G is called clique tree. The distance energy ED (G) of graph G is the sum of the absolute values of the eigenvalues of the distance matrix D(G). In this paper, we study the properties on the eigencomponents corresponding to the distance spectral radius of some special class of clique trees. Using this result we characterize a graph which gives the maximum distance spectral radius among all clique trees of order n with k cliques. From this result, we confirm a conjecture on the maximum distance energy, which was given in Lin et al. Linear Algebra Appl 467(2015) 29-39.",

keywords = "Distance energy, Distance matrix, Distance spectral radius",

author = "Shaowei Sun and Das, \{Kinkar Chandra\} and Yilun Shang",

note = "Publisher Copyright: {\textcopyright} 2021 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2021",

month = feb,

day = "2",

doi = "10.3390/math9040360",

language = "English",

volume = "9",

pages = "1--7",

journal = "Mathematics",

issn = "2227-7390",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

number = "4",

}

TY - JOUR

T1 - On maximal distance energy

AU - Sun, Shaowei

AU - Das, Kinkar Chandra

AU - Shang, Yilun

PY - 2021/2/2

Y1 - 2021/2/2

N2 - Let G be a graph of order n. If the maximal connected subgraph of G has no cut vertex then it is called a block. If each block of graph G is a clique then G is called clique tree. The distance energy ED (G) of graph G is the sum of the absolute values of the eigenvalues of the distance matrix D(G). In this paper, we study the properties on the eigencomponents corresponding to the distance spectral radius of some special class of clique trees. Using this result we characterize a graph which gives the maximum distance spectral radius among all clique trees of order n with k cliques. From this result, we confirm a conjecture on the maximum distance energy, which was given in Lin et al. Linear Algebra Appl 467(2015) 29-39.

AB - Let G be a graph of order n. If the maximal connected subgraph of G has no cut vertex then it is called a block. If each block of graph G is a clique then G is called clique tree. The distance energy ED (G) of graph G is the sum of the absolute values of the eigenvalues of the distance matrix D(G). In this paper, we study the properties on the eigencomponents corresponding to the distance spectral radius of some special class of clique trees. Using this result we characterize a graph which gives the maximum distance spectral radius among all clique trees of order n with k cliques. From this result, we confirm a conjecture on the maximum distance energy, which was given in Lin et al. Linear Algebra Appl 467(2015) 29-39.

KW - Distance energy

KW - Distance matrix

KW - Distance spectral radius

UR - https://www.scopus.com/pages/publications/85101079385

U2 - 10.3390/math9040360

DO - 10.3390/math9040360

M3 - Article

AN - SCOPUS:85101079385

SN - 2227-7390

VL - 9

SP - 1

EP - 7

JO - Mathematics

JF - Mathematics

IS - 4

M1 - 360

ER -

On maximal distance energy

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this