Comparative Study of Planar Octahedron Molecular Structure via Eccentric Invariants.

A branch of graph theory that makes use of a molecular graph is called chemical graph theory. Chemical graph theory is used to depict a chemical molecule. A graph is connected if there is an edge between every pair of vertices.

Laplacian and signless laplacian spectra and energies of multi-step wheels.

Energies and spectrum of graphs associated to different linear operators play a significant role in molecular chemistry, polymerisation, pharmacy, computer networking and communication systems. In current article, we compute closed forms of signless Laplacian and Laplacian spectra and energies of multi-step wheel networks . These wheel networks are useful in networking and communication, as every node is one hoop neighbour to other.

The Laplacian-Energy-Like Invariants of Three Types of Lattices.

This paper mainly studies the Laplacian-energy-like invariants of the modified hexagonal lattice, modified Union Jack lattice, and honeycomb lattice. By utilizing the tensor product of matrices and the diagonalization of block circulant matrices, we derive closed-form formulas expressing the Laplacian-energy-like invariants of these lattices. In addition, we obtain explicit asymptotic values of these invariants with software-aided computations of some integrals.