On Maximal Distance Energy

Shaowei Sun, Kinkar Chandra Das*, Yilun Shang*

*Corresponding author for this work

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Abstract

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 ED(G) of graph G is the sum of the absolute values of the eigenvalues of the distance matrix D(G). 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.
Original languageEnglish
Article number360
Pages (from-to)1-7
Number of pages7
JournalMathematics
Volume9
Issue number4
DOIs
Publication statusPublished - 11 Feb 2021

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