The energy of trees with diameter five under given conditions
type: Item
instance of: scholarly article
title: The energy of trees with diameter five under given conditions
DOI: 10.1007/978-3-030-97328-5_12
author: Yarong Jia
author: Qingsong Du
author: Bin Liu
author: Zijian Deng
author: Bofeng Huo
publication date: 2022-10-06T00:00:00Z
review text: Defined by \textit{I. Gutman} [The energy of a graph. Ber. Math.-Stat. Sekt. Forschungszent. Graz 103, 22 S. (1978; Zbl 0402.05040)] half a century ago, the energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Since then, many papers have characterised the structure of trees with various extremal or near-extremal energies. The present paper refines and extends studies of the relative energies of trees with diameter 5 in the papers [\textit{X. Qiao} and \textit{B. Huo}, ``Extremal energy of a class of tree with diameter five'', J. Qinghai Normal Univ. (Nat. Sci.), 2, 29--32 (2018); \textit{Y. Jia} and \textit{B. Huo}, ``The ordering of energies in a class of trees with diameter five'', ibid. 2 (2019)]. In particular, the present paper restricts these studies to a narrower class of trees of diameter~5 that contains the diameter 5 trees with maximal energy. The present authors provide details of the quasi-order on that class defined by the energy and show that the graphs in the class with larger energy have the properties that if two non-center vertices are adjacent to the same center, then the numbers of their pendent neighbors differ by at most one; whereas if two non-center vertices are adjacent to different centers, then the numbers of their pendent neighbors differ by at most two. For the entire collection see [Zbl 1493.37005].
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 31C20
zbMATH DE Number: 7597348
zbMATH Keywords: graph
zbMATH Keywords: energy
zbMATH Keywords: extremal
zbMATH Keywords: diameter
zbMATH Keywords: quasi-order
reviewed by: Thomas Britz
MaRDI profile type: Publication
full work available at URL: 978-3-030-97328-5 12
OpenAlex ID: W4288540247
cites work: Q5452542
cites work: Q4903449
cites work: More trees with large energy
cites work: On the minimal energy of trees with a given diameter
cites work: On acyclic molecular graphs with maximal Hosoya index, energy, and short diameter
cites work: On the tree with diameter 4 and maximal energy
cites work: Graph Energy
cites work: Q4186355
cites work: Q3760584
Recommended article: Minimum energy on trees with \(k\) pendent vertices
Recommended article: Q5471159
Recommended article: On the tree with diameter 4 and maximal energy
Recommended article: Q3377644
Recommended article: Q5159188
Recommended article: Q3144325
Recommended article: Energy of trees with edge independence number two
Recommended article: Q5452542
Recommended article: Maximum energy trees with two maximum degree vertices
Recommended article: Extremal energies of trees with a given domination number
description: scientific article; zbMATH DE number 7597348