EconPapers    
Economics at your fingertips  
 

Spectral and Sharp Sufficient Conditions for Graphs to Admit a Strong Star Factor

Fengyun Ren, Shumin Zhang () and He Li
Additional contact information
Fengyun Ren: School of Mathematics and Statistics, Qinghai Normal University, Xining 810001, China
Shumin Zhang: School of Mathematics and Statistics, Qinghai Normal University, Xining 810001, China
He Li: School of Information Engineering, Communication University of Shanxi, Jinzhou 030619, China

Mathematics, 2025, vol. 13, issue 10, 1-32

Abstract: Let G be a graph. An odd [ 1 , k ] -factor of a graph G is a spanning subgraph H of G such that d e g H ( v ) is odd and 1 ⩽ d e g H ( v ) ⩽ k for every v ∈ V ( G ) where k is a positive odd integer. We call a spanning subgraph H of a graph G a strong star factor if every component of H is isomorphic to an element of the stars K 1 , 1 , K 1 , 2 , ⋯ , K 1 , r and is an induced subgraph of G where r ⩾ 2 is an integer. In a { K 1 , 1 , K 1 , 2 , C m : m ⩾ 3 } -factor of G , each component is isomorphic to a member in { K 1 , 1 , K 1 , 2 , C 3 , C 4 ⋯ , C m } . A graph G is a strong star factor deleted graph if G − e has a strong star factor for each edge e of G . In this paper, through the typical spectral techniques, we obtain the respective necessary and sufficient conditions defining a strong star factor deleted graph, an odd [ 1 , k ] -factor deleted graph, and a { K 1 , 1 , K 1 , 2 , C m : m ⩾ 3 } -factor deleted graph. We determine a lower bound on the size to guarantee that G is a { K 1 , 1 , K 1 , 2 , C m : m ⩾ 3 } -factor deleted graph. We establish the upper bound of the signless Laplacian spectral radius (resp. the spectral radius) and the lower bound of the distance signless Laplacian spectral radius (resp. the distance spectral radius) to determine whether G admits a strong star factor. Furthermore, by constructing extremal graphs, we show that all the bounds obtained in this contribution are the best possible.

Keywords: strong star factor; odd [1, k ]-factor deleted graph; distance signless Laplacian spectral radius; signless Laplacian spectral radius; distance spectral radius (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/10/1640/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/10/1640/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:10:p:1640-:d:1657884

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().

 
Page updated 2025-05-17
Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1640-:d:1657884