RESUMO
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. A topological index is a numerical value related to the chemical structure that claims to show a relationship between chemical structure and various physicochemical attributes, chemical reactivity, or, you could say, biological activity. In this article, we examined the topological properties of a planar octahedron network of m dimensions and computed the total eccentricity, average eccentricity, Zagreb eccentricity, geometric arithmetic eccentricity, and atom bond connectivity eccentricity indices, which are used to determine the distance between the vertices of a planar octahedron network.
RESUMO
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 Wn,m. These wheel networks are useful in networking and communication, as every node is one hoop neighbour to other. We also present our results for wheel graphs as particular cases. In the end, correlation of these energies on the involved parameters m ≥ 3 and n is given graphically. Present results are the natural generalizations of the already available results in the literature.
RESUMO
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.
