For a connected graph G on n vertices, recall that the reciprocal distance signless Laplacian matrix of is defined to be RQ(G)=RT(G)+RD(G), where RD(G) matrix, RT(G)=diag(RT1,RT2,⋯,RTn) and RTi degree vertex vi. In 2022, generalized which by RDα(G)=αRT(G)+(1−α)RD(G),α∈[0,1], was introduced. this paper, we give some bounds spectral radius RDα(G) characterize its extremal graph. addition, also li...

In this paper, we show that the eigenvectors associated with the zero eigenvalues of the Laplacian and signless Lapacian tensors of a k-uniform hypergraph are closely related to some configured components of that hypergraph. We show that the components of an eigenvector associated with the zero eigenvalue of the Laplacian or signless Lapacian tensor have the same modulus. Moreover, under a cano...

In this paper, we show that the eigenvectors of the zero Laplacian and signless Lapacian eigenvalues of a k-uniform hypergraph are closely related to some configured components of that hypergraph. We show that the components of an eigenvector of the zero Laplacian or signless Lapacian eigenvalue have the same modulus. Moreover, under a canonical regularization, the phases of the components of t...

The spectral radius (or the signless Laplacian radius) of a general hypergraph is maximum modulus eigenvalues its adjacency Laplacian) tensor. In this paper, we firstly obtain lower bound hypergraphs in terms clique number. Moreover, present relation between homogeneous polynomial and number hypergraphs. As an application, finally upper

The component matrix, Laplacian Distance Peripheral distance of the cyclotomic graphs and some properties are found. D-energy, $D_{p}$-energy, $D^{L}$-energy indices determined. For real symmetric matrices, matrices that attain maximum $L, L_{s}$ minimum S calculated. Hausdorff optimal matching evaluated.