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Article

# On Maximal Distance Energy

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School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China
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Department of Mathematics, Sungkyunkwan University, Suwon 16419, Korea
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Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK
*
Authors to whom correspondence should be addressed.
Academic Editors: Pavel Trojovský, Diego Marques and Iwona Włoch
Mathematics 2021, 9(4), 360; https://doi.org/10.3390/math9040360
Received: 19 January 2021 / Revised: 7 February 2021 / Accepted: 9 February 2021 / Published: 11 February 2021
(This article belongs to the Special Issue New Insights in Algebra, Discrete Mathematics, and Number Theory)
Let G be a graph of order n. If the maximal connected subgraph of G has no cut vertex then it is called a block. If each block of graph G is a clique then G is called clique tree. The distance energy ${E}_{D}\left(G\right)$ of graph G is the sum of the absolute values of the eigenvalues of the distance matrix $D\left(G\right)$. In this paper, we study the properties on the eigencomponents corresponding to the distance spectral radius of some special class of clique trees. Using this result we characterize a graph which gives the maximum distance spectral radius among all clique trees of order n with k cliques. From this result, we confirm a conjecture on the maximum distance energy, which was given in Lin et al. Linear Algebra Appl 467(2015) 29-39. View Full-Text
MDPI and ACS Style

Sun, S.; Das, K.C.; Shang, Y. On Maximal Distance Energy. Mathematics 2021, 9, 360. https://doi.org/10.3390/math9040360

AMA Style

Sun S, Das KC, Shang Y. On Maximal Distance Energy. Mathematics. 2021; 9(4):360. https://doi.org/10.3390/math9040360

Chicago/Turabian Style

Sun, Shaowei, Kinkar C. Das, and Yilun Shang. 2021. "On Maximal Distance Energy" Mathematics 9, no. 4: 360. https://doi.org/10.3390/math9040360

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