There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Graph theory is vital for modeling and designing any chemical structure or network. Chemical graph theory is helpful to under first and about the structural characteristics of a molecular graph. Th...

The eccentric based Zagreb indices of carbon graphite

Mathematical chemistry is concerned with the use of mathematics to solve the problems in chemistry. A triangular chain graph is a simple graph composed of a series of triangles. This chain is widely used in the formation of triangular cactus, boron clusters, boron triangular nanotubes, and boron nanotubes. In this paper, the first Zagreb connection index, the first modified Zagreb connection index, and the second Zagreb connection index for triangular chain structures are calculated and derived closed formulas for them. Based on the derived formulas and obtained numerical results, the physicochemical properties of these type of structures can easily be investigated.

Zagreb connection topological descriptors and structural property of the triangular chain structures

Degree and distance-based graph polynomials are important not only as graph invariants but also for their applications in physics, chemistry, and pharmacy. The present paper is concerned with the H...

Base polynomials for degree and distance based topological invariants of n-bilinear straight pentachain

This paper deals with triangulations of the 2-torus with the vertex labeled general octahedral graph 4 O which is isomorphic to the complete four-partite graph 2,2,2,2 K ; it is known that there exist precisely twelve such triangulations. We find all the 12 triangulations in a Schlegel diagram of the hyperoctahedron and realize all of them geometrically with the same 1-skeleton in 3-space. In particular, we identify two geometric polyhedral tori (both without self-intersections) with the same 1-skeleton in 3-space, but without a single common face, or in other words their intersection (as point-sets) is only their common 1-skeleton. Similarly, all the twelve triangulations of the 2D projective plane with the vertex labeled complete graph 6 K are found in a Schlegel diagram of the 5-simplex and all are realized geometrically with the same 1-skeleton in 4-space; especially we obtain a pair of triangulations of the Möbius band and a pair of triangulated projective planes with the same 1-skeleton (within each pair) in 3-space and 4-space, respectively, without a single common face. The constructed polyhedra are modeled and visualized with GeoGebra. 2020 MATHEMATICS SUBJECT CLASSIFICATION: 52B70, 52B11, 05C10, 51M15, 51M20

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Old and new geometric polyhedra with few vertices

There are many topological indices which have been discussed so far But the most important topological indices among all these are topological degree-based indices Topological indices in QSAR/QSP

Aamna Amer

Papers

Edge version of topological degree based indices of Boron triangular nanotubes

Computational aspects of line graph of boron triangular nanotubes