-cospectrality and -energy in cographs. Issue 2 (1st February 2018)

• Record Type: Journal Article
• Authors: Tura, Fernando
• Is Part Of: Linear & multilinear algebra. Volume 66:Issue 2(2018)
• Page Start: 398
• Page End: 409
• Publication Date: 2018-02-01
• Subjects: Eigenvalue -- distance Laplacian matrix -- distance signless Laplacian matrix -- cographs; 15A18 -- 05C50 -- 05C85; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2017.1300230
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : The distance Laplacian matrix of a connected graph G is defined to be where denotes the distance matrix of G and diag( Tr ) denotes the diagonal matrix of the vertex transmissions in G . Similarly, the distance signless Laplacian matrix of G is defined as In this paper, we present a large set of nonisomorphic graphs which are -cospectral. A simple construction of graphs which are nonisomorphic and | L |-cospectral, where | L | is the signless Laplacian matrix of G, is also presented. We finish this paper exhibiting nonisomorphic and -noncospectral graphs with same -energy.