Some degree and distance-based invariants of wreath products of graphs

被引：7

作者：

Cavaleri, Matteo ^{[1
]}

Donno, Alfredo ^{[1
]}

机构：

[1] Univ Niccolo Cusano, Via Don Carlo Gnocchi 3, I-00166 Rome, Italy

来源：

DISCRETE APPLIED MATHEMATICS | 2020年 / 277卷

关键词：

Wreath product of graphs; Distance; Diameter; Antipodal graph; Zagreb indices; Wiener index; Szeged index; WIENER INDEX; ZAGREB INDEXES; ZIGZAG PRODUCT;

D O I：

10.1016/j.dam.2019.09.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The wreath product of graphs is a graph composition inspired by the notion of wreath product of groups, with interesting connections with Geometric Group Theory and Probability. This paper is devoted to the description of some degree and distance-based invariants, of large interest in Chemical Graph Theory, for a wreath product of graphs. An explicit formula is obtained for the Zagreb indices, in terms of the Zagreb indices of the factor graphs. A detailed analysis of distances in a wreath product is performed, allowing to describe the antipodal graph and to provide a formula for the Wiener index. Finally, a formula for the Szeged index is obtained. Several explicit examples are given. (C) 2019 Elsevier B.V. All rights reserved.

引用

页码：22 / 43

页数：22

共 36 条

[1] Semi-direct product in groups and Zig-zag product in graphs: Connections and applications [J].

Alon, N ;

Lubotzky, A ;

Wigderson, A .

42ND ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, PROCEEDINGS, 2001, :630-637

[2]

Assari A., 2017, PALEST J MATH, V6, P412

[3]

BAILEY RA, 1983, P LOND MATH SOC, V47, P69

[4] SPECTRAL ANALYSIS OF THE WREATH PRODUCT OF A COMPLETE GRAPH WITH A COCKTAIL PARTY GRAPH [J].

Belardo, Francesco ;

Cavaleri, Matteo ;

Donno, Alfredo .

ATTI ACCADEMIA PELORITANA DEI PERICOLANTI-CLASSE DI SCIENZE FISICHE MATEMATICHE E NATURALI, 2018, 96 :A11-A111

[5] Wreath product of a complete graph with a cyclic graph: Topological indices and spectrum [J].

Belardo, Francesco ;

Cavaleri, Matteo ;

Donno, Alfredo .

APPLIED MATHEMATICS AND COMPUTATION, 2018, 336 :288-300

[6] VERTEX AND EDGE TRANSITIVE, BUT NOT 1-TRANSITIVE, GRAPHS [J].

BOUWER, IZ .

CANADIAN MATHEMATICAL BULLETIN, 1970, 13 (02) :231-&

[7]

Burillo J., ARXIV150606935MATHGR

[8] Wreath product of matrices [J].

D'Angeli, Daniele ;

Donno, Alfredo .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2017, 513 :276-303

[9] Connectedness and Isomorphism Properties of the Zig-Zag Product of Graphs [J].

D'Angeli, Daniele ;

Donno, Alfredo ;

Sava-Huss, Ecaterina .

JOURNAL OF GRAPH THEORY, 2016, 83 (02) :120-151

[10] Relative subgroup growth and subgroup distortion [J].

Davis, Tara C. ;

Olshanskii, Alexander Yu. .

GROUPS GEOMETRY AND DYNAMICS, 2015, 9 (01) :237-273

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