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ON THE SIZE, SPECTRAL RADIUS, DISTANCE SPECTRAL RADIUS AND FRACTIONAL MATCHINGS IN GRAPHS

Part of: Basic linear algebra Graph theory

Published online by Cambridge University Press:  13 January 2023

SHUCHAO LI Open the ORCID record for SHUCHAO LI [Opens in a new window] ,
SHUJING MIAO Open the ORCID record for SHUJING MIAO [Opens in a new window]  and
MINJIE ZHANG Open the ORCID record for MINJIE ZHANG [Opens in a new window]
SHUCHAO LI
Affiliation:
Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, PR China e-mail: [email protected]
SHUJING MIAO
Affiliation:
Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, PR China e-mail: [email protected]
MINJIE ZHANG*
Affiliation:
School of Mathematics and Statistics, Hubei University of Arts and Science, Xiangyang 441053, PR China
*
e-mail: [email protected]
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Abstract

We first establish a lower bound on the size and spectral radius of a graph G to guarantee that G contains a fractional perfect matching. Then, we determine an upper bound on the distance spectral radius of a graph G to ensure that G has a fractional perfect matching. Furthermore, we construct some extremal graphs to show all the bounds are best possible.

Keywords

sizespectral radiusdistance spectral radiusfractional perfect matching

MSC classification

Primary: 05C75: Structural characterization of families of graphs
Secondary: 05C31: Graph polynomials 15A18: Eigenvalues, singular values, and eigenvectors
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 108 , Issue 2 , October 2023 , pp. 187 - 199
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The first author acknowledges the financial support from the National Natural Science Foundation of China (Grant Nos. 12171190, 11671164) and the third author acknowledges the financial support from the National Natural Science Foundation of China (Grant No. 11901179).

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