No abstract

In this work, the Seidel Laplacian spectrum of graphs are determined. Then new bounds are presented for the Seidel Laplacian energy of regular graphs and graphs by using their Seidel Laplacian spectrum and other techniques. Further, the Seidel Laplacian energy of specific graphs are computed.

In this paper, skew ABC matrix and its energy are introduced for digraphs. Firstly, some fundamental spectral features of the skew ABC matrix of digraphs are established. Then some upper and lower bounds are presented for the skew ABC energy of digraphs. Further extremal digraphs are determined attaining these bounds.

The matrix representations of hypergraphs have been defined via hypermatrices initially. In recent studies, the Laplacian matrix of hypergraphs, a generalization of the Laplacian matrix, has been introduced. In this article, based on this definition, we derive bounds depending pair-degree, maximum degree, and the first Zagreb index for the greatest Laplacian eigenvalue and Laplacian energy of r-uniform hypergraphs and r-uniform regular hypergraphs. As a result of these bounds, Nordhaus–Gaddum type bounds are obtained for the Laplacian energy.

In this article, degree distance of zero-divisor graph Г[ℤ ] is computed for = , = and = , where , are distinct prime numbers.