Extremal Results for Cacti

Muhuo Liu; Yuedan Yao; Kinkar Chandra Das

doi:10.1007/s40840-019-00837-2

Extremal Results for Cacti

Muhuo Liu
, Yuedan Yao
, Kinkar Chandra Das

Department of Mathematics

South China Agricultural University

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

7 Scopus citations

Abstract

In this paper, we determine the unique maximum (or minimum) extremal graph for general spectral radius, zeroth-order general Randić index, general sum-connectivity index, general Platt index, second Zagreb index and multiplicative Zagreb indices in the class of cacti with n≥ 4 vertices and k≥ 0 cycles. By applying our new result, we demonstrate the unique maximum extremal graph for general spectral radius, zeroth-order general Randić index, general sum-connectivity index, general Platt index, second Zagreb index and second multiplicative Zagreb index in the class of cacti with n≥ 4 vertices. Furthermore, we also determine the unified maximum extremal graphs for general spectral radius, zeroth-order general Randić index and the second multiplicative Zagreb index in the class of cacti with n≥ 4 vertices and k≥ 1 pendant vertices.

Original language	English
Pages (from-to)	2783-2798
Number of pages	16
Journal	Bulletin of the Malaysian Mathematical Sciences Society
Volume	43
Issue number	3
DOIs	https://doi.org/10.1007/s40840-019-00837-2
State	Published - 1 May 2020

Keywords

Cactus graph
Extremal graph
General Platt index
General sum-connectivity index
Zeroth-order general Randić index

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10.1007/s40840-019-00837-2

Cite this

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title = "Extremal Results for Cacti",

abstract = "In this paper, we determine the unique maximum (or minimum) extremal graph for general spectral radius, zeroth-order general Randi{\'c} index, general sum-connectivity index, general Platt index, second Zagreb index and multiplicative Zagreb indices in the class of cacti with n≥ 4 vertices and k≥ 0 cycles. By applying our new result, we demonstrate the unique maximum extremal graph for general spectral radius, zeroth-order general Randi{\'c} index, general sum-connectivity index, general Platt index, second Zagreb index and second multiplicative Zagreb index in the class of cacti with n≥ 4 vertices. Furthermore, we also determine the unified maximum extremal graphs for general spectral radius, zeroth-order general Randi{\'c} index and the second multiplicative Zagreb index in the class of cacti with n≥ 4 vertices and k≥ 1 pendant vertices.",

keywords = "Cactus graph, Extremal graph, General Platt index, General sum-connectivity index, Zeroth-order general Randi{\'c} index",

author = "Muhuo Liu and Yuedan Yao and Das, \{Kinkar Chandra\}",

note = "Publisher Copyright: {\textcopyright} 2019, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.",

year = "2020",

month = may,

day = "1",

doi = "10.1007/s40840-019-00837-2",

language = "English",

volume = "43",

pages = "2783--2798",

journal = "Bulletin of the Malaysian Mathematical Sciences Society",

issn = "0126-6705",

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TY - JOUR

T1 - Extremal Results for Cacti

AU - Liu, Muhuo

AU - Yao, Yuedan

AU - Das, Kinkar Chandra

PY - 2020/5/1

Y1 - 2020/5/1

N2 - In this paper, we determine the unique maximum (or minimum) extremal graph for general spectral radius, zeroth-order general Randić index, general sum-connectivity index, general Platt index, second Zagreb index and multiplicative Zagreb indices in the class of cacti with n≥ 4 vertices and k≥ 0 cycles. By applying our new result, we demonstrate the unique maximum extremal graph for general spectral radius, zeroth-order general Randić index, general sum-connectivity index, general Platt index, second Zagreb index and second multiplicative Zagreb index in the class of cacti with n≥ 4 vertices. Furthermore, we also determine the unified maximum extremal graphs for general spectral radius, zeroth-order general Randić index and the second multiplicative Zagreb index in the class of cacti with n≥ 4 vertices and k≥ 1 pendant vertices.

AB - In this paper, we determine the unique maximum (or minimum) extremal graph for general spectral radius, zeroth-order general Randić index, general sum-connectivity index, general Platt index, second Zagreb index and multiplicative Zagreb indices in the class of cacti with n≥ 4 vertices and k≥ 0 cycles. By applying our new result, we demonstrate the unique maximum extremal graph for general spectral radius, zeroth-order general Randić index, general sum-connectivity index, general Platt index, second Zagreb index and second multiplicative Zagreb index in the class of cacti with n≥ 4 vertices. Furthermore, we also determine the unified maximum extremal graphs for general spectral radius, zeroth-order general Randić index and the second multiplicative Zagreb index in the class of cacti with n≥ 4 vertices and k≥ 1 pendant vertices.

KW - Cactus graph

KW - Extremal graph

KW - General Platt index

KW - General sum-connectivity index

KW - Zeroth-order general Randić index

UR - https://www.scopus.com/pages/publications/85073919653

U2 - 10.1007/s40840-019-00837-2

DO - 10.1007/s40840-019-00837-2

M3 - Article

AN - SCOPUS:85073919653

SN - 0126-6705

VL - 43

SP - 2783

EP - 2798

JO - Bulletin of the Malaysian Mathematical Sciences Society

JF - Bulletin of the Malaysian Mathematical Sciences Society

IS - 3

ER -

Extremal Results for Cacti

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Keywords

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