On Maximal Distance Energy - Shaowei Sun; Kinkar Chandra Das; Yilun Shang (Mathematics, 2021)
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 <semantics>ED(G)</semantics> of graph G is the sum of the absolute values of the eigenvalues of the distance matrix <semantics>D(G)</semantics>. 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.