Sharp bounds on the distance spectral radius and the distance energy of graphs

By Gopalapillai Indulal. 2009

128 citations recorded by the source corpus.

The D-eigenvalues {μ1,μ2,…,…,μp} of a graph G are the eigenvalues of its distance matrix D and form the D-spectrum of G denoted by specD(G). The greatest D-eigenvalue is called the D-spectral radius of G denoted by μ1. The D-energy ED(G) of the graph G is the sum of the absolute values of its D-eigenvalues. In this paper we obtain some lower bounds for μ1 and characterize those graphs for which these bounds are best possible. We also obtain an upperbound for ED(G) and determine those maximal D-energy graphs.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/192d13e540f4072c3b4e9f1d4cdd1359b66367f6

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In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

Randic Spectral Radius and Randic Energy (2010, result): “Proof is similar to that of Lemma 2 in [7].”
On Distance Spectral Radius and Distance Energy of Graphs (2011, background): “Lower and upper bounds for distance energy have been obtained in [15–19].”