Affiliation:
1. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510090, China
2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
Abstract
<abstract><p>The $ \epsilon $-spectral radius of a connected graph is the largest eigenvalue of its eccentricity matrix. In this paper, we identify the unique $ n $-vertex tree with diameter $ 4 $ and matching number $ 5 $ that minimizes the $ \epsilon $-spectral radius, and thus resolve a conjecture proposed in [W. Wei, S. Li, L. Zhang, Characterizing the extremal graphs with respect to the eccentricity spectral radius, and beyond, Discrete Math. 345 (2022) 112686].</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference17 articles.
1. A. Alhevaz, M. Baghipur, Y. Shang, Merging the spectral theories of distance Estrada and distance signless Laplacian Estrada indices of graphs, Mathematics, 7 (2019), 995. https://doi.org/10.3390/math7100995
2. M. Aouchiche, P. Hansen, Distance spectra of graphs: a survey, Linear Algebra Appl., 458 (2014), 301–386. https://doi.org/10.1016/j.laa.2014.06.010
3. R. B. Bapat, Graphs and matrices, 2 Eds., London: Springer, 2014. https://doi.org/10.1007/978-1-4471-6569-9
4. A. E. Brouwer, W. H. Haemers, Spectra of graphs, New York: Springer, 2012. https://doi.org/10.1007/978-1-4614-1939-6
5. X. He, L. Lu, On the largest and least eigenvalues of eccentricity matrix of trees, Discrete Math., 345 (2022), 112662. https://doi.org/10.1016/j.disc.2021.112662
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2 articles.
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