Solution to a conjecture on the maximum ABC index of graphs with given chromatic number

Xiaodan Chen; Kinkar Ch Das

doi:10.1016/j.dam.2018.05.063

Solution to a conjecture on the maximum ABC index of graphs with given chromatic number

Xiaodan Chen, Kinkar Ch Das

Department of Mathematics

Guangxi University

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

10 Scopus citations

Abstract

The atom-bond connectivity (ABC) index of a graph G = (V,E) is defined as [Formula presented]where d_u,d_v are the degrees of the vertices u and v in G, respectively. In this paper, we prove that among all n-vertex graphs with given chromatic number χ≥3, the Turán graph [Formula presented] is the unique graph having the maximum ABC index, which completely confirms a conjecture posed in Zhang et al. (2016).

Original language	English
Pages (from-to)	126-134
Number of pages	9
Journal	Discrete Applied Mathematics
Volume	251
DOIs	https://doi.org/10.1016/j.dam.2018.05.063
State	Published - 31 Dec 2018

Keywords

Chromatic number
Maximum ABC index
Turán graph

Access to Document

10.1016/j.dam.2018.05.063

Cite this

@article{28bcb091da704e05a8435d8657c86d70,

title = "Solution to a conjecture on the maximum ABC index of graphs with given chromatic number",

abstract = "The atom-bond connectivity (ABC) index of a graph G = (V,E) is defined as [Formula presented]where du,dv are the degrees of the vertices u and v in G, respectively. In this paper, we prove that among all n-vertex graphs with given chromatic number χ≥3, the Tur{\'a}n graph [Formula presented] is the unique graph having the maximum ABC index, which completely confirms a conjecture posed in Zhang et al. (2016).",

keywords = "Chromatic number, Maximum ABC index, Tur{\'a}n graph",

author = "Xiaodan Chen and Das, \{Kinkar Ch\}",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

year = "2018",

month = dec,

day = "31",

doi = "10.1016/j.dam.2018.05.063",

language = "English",

volume = "251",

pages = "126--134",

journal = "Discrete Applied Mathematics",

issn = "0166-218X",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Solution to a conjecture on the maximum ABC index of graphs with given chromatic number

AU - Chen, Xiaodan

AU - Das, Kinkar Ch

PY - 2018/12/31

Y1 - 2018/12/31

N2 - The atom-bond connectivity (ABC) index of a graph G = (V,E) is defined as [Formula presented]where du,dv are the degrees of the vertices u and v in G, respectively. In this paper, we prove that among all n-vertex graphs with given chromatic number χ≥3, the Turán graph [Formula presented] is the unique graph having the maximum ABC index, which completely confirms a conjecture posed in Zhang et al. (2016).

AB - The atom-bond connectivity (ABC) index of a graph G = (V,E) is defined as [Formula presented]where du,dv are the degrees of the vertices u and v in G, respectively. In this paper, we prove that among all n-vertex graphs with given chromatic number χ≥3, the Turán graph [Formula presented] is the unique graph having the maximum ABC index, which completely confirms a conjecture posed in Zhang et al. (2016).

KW - Chromatic number

KW - Maximum ABC index

KW - Turán graph

UR - https://www.scopus.com/pages/publications/85048393808

U2 - 10.1016/j.dam.2018.05.063

DO - 10.1016/j.dam.2018.05.063

M3 - Article

AN - SCOPUS:85048393808

SN - 0166-218X

VL - 251

SP - 126

EP - 134

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Solution to a conjecture on the maximum ABC index of graphs with given chromatic number

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this