Distance Laplacian spectra of graphs: A survey

The distance matrix D of a connected graph G is the matrix indexed by the vertices of G where Di,j = d(vi, vj) and d(vi, vj) denotes the distance between the vertices vi and vj. The distance Laplacian of a connected graph G is defined as DL = Diag(Tr) - D, where Diag(Tr) denotes the diagonal matrix of the vertex transmissions in G. The concepts of distance Laplacian matrix is motived by the Laplacian matrix, first introduced in 2013 and has attracted the attention of several researchers in Algebraic Graph Theory. Their spectral investigation led to a considerable number of publications. In this paper, we present a survey of work about distance Laplacian of a connected graphs. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.