An independent set degree condition for fractional critical deleted graphs

Wei Gao; Juan Luis García Guirao; Mahmoud Abdel-Aty; Wenfei Xi

doi:10.3934/dcdss.2019058

Article Contents

2019, Volume 12, Issue 4&5: 877-886. Doi: 10.3934/dcdss.2019058 open access

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An independent set degree condition for fractional critical deleted graphs

1.
School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China
2.
Departamento de Matemática Aplicaday Estadística, Universidad Politécnica de Cartagena, Hospital de Marina, 30203-Cartagena, Región de Murcia, Spain
3.
Center for Photonics and Smart Materials (CPSM), Zewail City of Science and Technology, Egypt
4.
Mathematics Department, Faculty of Sciences, Sohag University, Egypt
5.
Communication and Networks Engineering, Gulf University, Kingdom of Bahrain
6.
College of Tourism and Geographic Sciences, Yunnan Normal University, Kunming 650500, China

* Corresponding author: Wei Gao(gaowei@ynnu.edu.cn)
* Corresponding author: Wei Gao(gaowei@ynnu.edu.cn)

Received: October 31, 2017

Revised: December 31, 2017

Published: March 2019

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Abstract

Let $i≥2$, $Δ≥0$, $1≤ a≤ b-Δ$, $n>\frac{(a+b)(ib+2m-2)}{a}+n'$ and $δ(G)≥\frac{b^{2}}{a}+n'+2m$, and let $g,f$ be two integer-valued functions defined on $V(G)$ such that $a≤ g(x)≤ f(x)-Δ≤ b-Δ$ for each $x∈ V(G)$. In this article, it is determined that $G$ is a fractional $(g,f,n',m)$-critical deleted graph if $\max\{d_{1},d_{2},···,d_{i}\}≥\frac{b(n+n')}{a+b}$ for any independent subset $\{x_{1},x_{2},..., x_{i}\}\subseteq V(G)$. The result is tight on independent set degree condition.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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References

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