Maxima of the Q-index for 3K3-free graphs

Yanting Zhang; Ligong Wang

doi:10.1016/j.dam.2024.08.004

Maxima of the Q-index for 3K₃-free graphs

Yanting Zhang
, Ligong Wang

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

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

Abstract

The Q-index of a graph G is the largest eigenvalue of its Q-matrix Q(G)=D(G)+A(G), where D(G) and A(G) are the diagonal matrix of vertex degrees and the adjacency matrix of G, respectively. Let 3K₃ denote the graph consisting of three vertex-disjoint triangles. A graph is called 3K₃-free if it does not contain 3K₃ as a subgraph. In this paper, we present a sharp upper bound on the Q-index of 3K₃-free graphs of order n≥453, and characterize the unique extremal graph which attains the bound.

Original language	English
Pages (from-to)	448-456
Number of pages	9
Journal	Discrete Applied Mathematics
Volume	358
DOIs	https://doi.org/10.1016/j.dam.2024.08.004
State	Published - 15 Dec 2024

Keywords

3K-free graphs
Extremal graph
Q-index
Q-matrix

Access to Document

10.1016/j.dam.2024.08.004

Cite this

@article{979a2aa47af7460bbd01ce269b493c23,

title = "Maxima of the Q-index for 3K3-free graphs",

abstract = "The Q-index of a graph G is the largest eigenvalue of its Q-matrix Q(G)=D(G)+A(G), where D(G) and A(G) are the diagonal matrix of vertex degrees and the adjacency matrix of G, respectively. Let 3K3 denote the graph consisting of three vertex-disjoint triangles. A graph is called 3K3-free if it does not contain 3K3 as a subgraph. In this paper, we present a sharp upper bound on the Q-index of 3K3-free graphs of order n≥453, and characterize the unique extremal graph which attains the bound.",

keywords = "3K-free graphs, Extremal graph, Q-index, Q-matrix",

author = "Yanting Zhang and Ligong Wang",

note = "Publisher Copyright: {\textcopyright} 2024 Elsevier B.V.",

year = "2024",

month = dec,

day = "15",

doi = "10.1016/j.dam.2024.08.004",

language = "英语",

volume = "358",

pages = "448--456",

journal = "Discrete Applied Mathematics",

issn = "0166-218X",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Maxima of the Q-index for 3K3-free graphs

AU - Zhang, Yanting

AU - Wang, Ligong

PY - 2024/12/15

Y1 - 2024/12/15

N2 - The Q-index of a graph G is the largest eigenvalue of its Q-matrix Q(G)=D(G)+A(G), where D(G) and A(G) are the diagonal matrix of vertex degrees and the adjacency matrix of G, respectively. Let 3K3 denote the graph consisting of three vertex-disjoint triangles. A graph is called 3K3-free if it does not contain 3K3 as a subgraph. In this paper, we present a sharp upper bound on the Q-index of 3K3-free graphs of order n≥453, and characterize the unique extremal graph which attains the bound.

AB - The Q-index of a graph G is the largest eigenvalue of its Q-matrix Q(G)=D(G)+A(G), where D(G) and A(G) are the diagonal matrix of vertex degrees and the adjacency matrix of G, respectively. Let 3K3 denote the graph consisting of three vertex-disjoint triangles. A graph is called 3K3-free if it does not contain 3K3 as a subgraph. In this paper, we present a sharp upper bound on the Q-index of 3K3-free graphs of order n≥453, and characterize the unique extremal graph which attains the bound.

KW - 3K-free graphs

KW - Extremal graph

KW - Q-index

KW - Q-matrix

UR - https://www.scopus.com/pages/publications/85201467882

U2 - 10.1016/j.dam.2024.08.004

DO - 10.1016/j.dam.2024.08.004

M3 - 文章

AN - SCOPUS:85201467882

SN - 0166-218X

VL - 358

SP - 448

EP - 456

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Maxima of the Q-index for 3K₃-free graphs

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this