Several topological indices are known to have widespread implications in a variety of research areas. Over the years, Kirchhoff index has turned out be an extremely significant and efficient index. In this paper, we propose exact formulas for expected values random polyomino chain construct multiplicative degree-Kirchhoff additive We also carefully examine highest degree through

The technique of securing information or data in the form images, codes, merging words etc are closely related to disciplines cryptanalysis and cryptology. Analogous this numerical encoding chemical structure, connected topological indices is also growing significantly field graph theory. One salient features predict characteristics prescribed by molecule's structure. In paper, we calculate two...

The interplay between quantization and topology is investigated in the frame of a topological model of electromagnetism proposed by the author. In that model, the energy of electromagnetic radiation in a cubic cavity is E = (d/4)h̄ω where d is a topological integer index equal to the degree of a map between two orbifolds. To be published in Physics Letters A PACS: 11.10; 03.50; 02.40; 41.10

By using φ-mapping method, we discuss the topological structure of the self-duality solution in Jackiw-Pi model in terms of gauge potential decomposition. We set up relationship between Chern-Simons vortex solution and topological number which is determined by Hopf index and Brouwer degree. We also give the quantization of flux in this case. Then, we study the angular momentum of the vortex, it...

By using φ-mapping method, we discuss the topological structure of the self-duality solution in Jackiw-Pi model in terms of gauge potential decomposition. We set up relationship between Chern-Simons vortex solution and topological number which is determined by Hopf index and Brouwer degree. We also give the quantization of flux in this case. Then, we study the angular momentum of the vortex, it...

Let $d_G(v)$ be the degree of vertex $v$ in a graph $G$. The Sombor index $G$ is defined as $SO(G) =\sum_{uv\in E(G)}\sqrt{d^2_G(u)+d^2_G(v)}$, which new degree-based topological introduced by Gutman. $\mathscr{T}_{n,\Delta}$ and $\mathscr{U}_{n,\Delta}$ set trees unicyclic graphs with $n$ vertices maximum $\Delta$, respectively. In this paper, tree minimum among are characterized.

We study the persistence of eigenvalues and eigenvectors perturbed eigenvalue problems in Hilbert spaces. assume that unperturbed problem has a nontrivial kernel odd dimension we prove Rabinowitz-type global continuation result. The approach is topological, based on notion degree for oriented Fredholm maps index zero between real differentiable Banach manifolds.

in this paper, some applications of our earlier results in working with chemical graphs arepresented.