Signless Laplacian energy, distance Laplacian energy and distance signless Laplacian spectrum of unitary addition Cayley graphs

Graphs Defined on Rings: A Review

“…The signless Laplacian energy of the unitary addition Cayley graph was also independently examined in [209], which again had the same results as similar proof techniques.…”

“…Apart form the study of these computational parameters, the spectra associated with different matrices defined on the graph, along with their corresponding spectral properties, were investigated in [208][209][210][211]. In [210], spectral studies related to the adjacency and the Laplacian matrix were conducted, where the eigenvalues and the Laplacian eigenvalues of the unitary addition Cayley graph X + n and its complement X + n were determined.…”

“…In [209], along with the signless Laplacian energy, other derived forms of Laplacian energies such as the distance Laplacian and the signless distance Laplacian energy for the unitary addition Cayley graphs were investigated. The distance Laplacian energy and the signless distance Laplacian energy of a graph are the sum of the absolute values of the eigenvalues of the distance Laplacian and the signless distance Laplacian matrix, respectively.…”

“…The distance Laplacian energy and the signless distance Laplacian energy of a graph are the sum of the absolute values of the eigenvalues of the distance Laplacian and the signless distance Laplacian matrix, respectively. The distance Laplacian matrix and the signless distance Laplacian matrix are correspondingly given as D(v) − Dis(G) and D(v) + Dis(G), where Dis(G) denotes the distance matrix of the graph G, and D(v) denotes the diagonal matrix in which each diagonal element corresponding to a vertex v is the sum of the shortest distances from the vertex v to all the vertices of the graph (refer to [209]).…”