NDLI: Unicyclic graphs of minimal spectral radius

Content Provider	Springer Nature Link
Author	Shi, Ling Sheng
Copyright Year	2013
Abstract	It was conjectured by Li and Feng in 1979 that the unicyclic graph formed by a cycle of order g linking to an endvertex of a path of length k minimizes the spectral radius of all unicyclic graphs of order g+k and girth g. In 1987, Cao proved that this conjecture is true for k ≥ g(g − 2)/8 and false for k = 2 and sufficiently large g. In this note, we show that g > 12 suffices for the counterexample and give more counterexamples with large girth for any integer k > 1.
Ending Page	286
Page Count	6
Starting Page	281
File Format	PDF
ISSN	14398516
e-ISSN	14397617
Journal	Acta Mathematica Sinica, English Series
Issue Number	2
Volume Number	29
Language	English
Publisher	Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Publisher Date	2013-01-15
Publisher Place	Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	unicyclic Extremal graph Li-Feng’s conjecture Mathematics spectral radius Graphs and linear algebra (matrices, eigenvalues, etc.)
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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Unicyclic graphs of minimal spectral radius