Signed graphs Gσ with nullity n(Gσ)−g(Gσ)−1

Suliman Khan

doi:10.1016/j.laa.2025.08.017

Signed graphs G^σ with nullity n(G^σ)−g(G^σ)−1

Suliman Khan

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

3 Scopus citations

Abstract

Let G^σ=(G,σ) be a signed graph of order n(G^σ). Let denote the girth, rank, and nullity of G^σ by g(G^σ), r(G^σ), and η(G^σ), respectively. Recently, Chang and Li (2022) [6], characterized connected graphs G with nullity n(G)−g(G)−1. In this paper, we extend the results of Chang and Li to the setting of signed graphs with some new improvements. Furthermore, we characterize signed graphs G^σ that satisfy the nullity conditions η(G^σ)=n(G^σ)−g(G^σ) and η(G^σ)=n(G^σ)−g(G^σ)−2, providing distinct characterization from those of Q. Wu et al. (2022).

Original language	English
Pages (from-to)	47-62
Number of pages	16
Journal	Linear Algebra and Its Applications
Volume	728
DOIs	https://doi.org/10.1016/j.laa.2025.08.017
State	Published - 1 Jan 2026
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2025 Elsevier Inc.

Keywords

Girth
Nullity
Rank
Signed graph
Switching equivalent

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

Access to Document

10.1016/j.laa.2025.08.017

Cite this

@article{48093643a7d4467a99f293686786ec0c,

title = "Signed graphs Gσ with nullity n(Gσ)−g(Gσ)−1",

abstract = "Let Gσ=(G,σ) be a signed graph of order n(Gσ). Let denote the girth, rank, and nullity of Gσ by g(Gσ), r(Gσ), and η(Gσ), respectively. Recently, Chang and Li (2022) [6], characterized connected graphs G with nullity n(G)−g(G)−1. In this paper, we extend the results of Chang and Li to the setting of signed graphs with some new improvements. Furthermore, we characterize signed graphs Gσ that satisfy the nullity conditions η(Gσ)=n(Gσ)−g(Gσ) and η(Gσ)=n(Gσ)−g(Gσ)−2, providing distinct characterization from those of Q. Wu et al. (2022).",

keywords = "Girth, Nullity, Rank, Signed graph, Switching equivalent",

author = "Suliman Khan",

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier Inc.",

year = "2026",

month = jan,

day = "1",

doi = "10.1016/j.laa.2025.08.017",

language = "English",

volume = "728",

pages = "47--62",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - Signed graphs Gσ with nullity n(Gσ)−g(Gσ)−1

AU - Khan, Suliman

PY - 2026/1/1

Y1 - 2026/1/1

N2 - Let Gσ=(G,σ) be a signed graph of order n(Gσ). Let denote the girth, rank, and nullity of Gσ by g(Gσ), r(Gσ), and η(Gσ), respectively. Recently, Chang and Li (2022) [6], characterized connected graphs G with nullity n(G)−g(G)−1. In this paper, we extend the results of Chang and Li to the setting of signed graphs with some new improvements. Furthermore, we characterize signed graphs Gσ that satisfy the nullity conditions η(Gσ)=n(Gσ)−g(Gσ) and η(Gσ)=n(Gσ)−g(Gσ)−2, providing distinct characterization from those of Q. Wu et al. (2022).

AB - Let Gσ=(G,σ) be a signed graph of order n(Gσ). Let denote the girth, rank, and nullity of Gσ by g(Gσ), r(Gσ), and η(Gσ), respectively. Recently, Chang and Li (2022) [6], characterized connected graphs G with nullity n(G)−g(G)−1. In this paper, we extend the results of Chang and Li to the setting of signed graphs with some new improvements. Furthermore, we characterize signed graphs Gσ that satisfy the nullity conditions η(Gσ)=n(Gσ)−g(Gσ) and η(Gσ)=n(Gσ)−g(Gσ)−2, providing distinct characterization from those of Q. Wu et al. (2022).

KW - Girth

KW - Nullity

KW - Rank

KW - Signed graph

KW - Switching equivalent

UR - https://www.scopus.com/pages/publications/105014271138

U2 - 10.1016/j.laa.2025.08.017

DO - 10.1016/j.laa.2025.08.017

M3 - Article

AN - SCOPUS:105014271138

SN - 0024-3795

VL - 728

SP - 47

EP - 62

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -