On the second largest distance eigenvalue of a graph. Issue 5 (4th May 2017)

• Record Type: Journal Article
• Authors: Liu, Ruifang; Xue, Jie; Guo, Litao
• Is Part Of: Linear & multilinear algebra. Volume 65:Issue 5(2017)
• Page Start: 1011
• Page End: 1021
• Publication Date: 2017-05-04
• Subjects: Distance matrix -- the second largest distance eigenvalue -- D-spectrum determined; 05C50 -- 05C12; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2016.1221376
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : Let G be a simple connected graph of order n and D ( G ) be the distance matrix of G . Suppose that is the distance spectrum of G . A graph G is said to be determined by its D -spectrum if any graph with the same distance spectrum as G is isomorphic to G . In this paper, we consider spectral characterization on the second largest distance eigenvalue of graphs, and prove that the graphs with are determined by their D -spectra.