arXiv subjects
Publications and source records attributed to Abdul Rauf Nizami.
This paper aims to develop the mathematical representation of a surface generated by elliptical arcs joining the sides of a regular polygon to a point lying vertically upward on the central axis of the polygon. The volume of the corresponding solid has also been determined.
Let $L_{n}$ be the molecular graph of linear $[n]$phenylene, and $L'_{n}$ the graph obtained by attaching 4-membered cycles to terminal hexagons of $L_{n-1}$. Thus, $L'_{n}$ is the molecular graph of the $α,ω$ - dicyclobutadieno derivative of $[n-1]$phenylene, containing $n-1$ hexagons and $n$ squares. In this paper we give polynomials which serve as bases for Schultz invariants. Actually, we represent lengths of paths among vertices of degrees 2-2, 2-3, and 3-3 of $L_{n}$ and $L'_{n}$ in terms of polynomials, which are used to find Schultz polynomial, modified Schultz polynomial, Schultz index, and modified Schultz index.
The Hosoya polynomial of a graph $G$ was introduced by H. Hosoya in 1988 as a counting polynomial, which actually counts the number of distances of paths of different lengths in $G$. The most interesting application of the Hosoya polynomial is that almost all distance-based graph invariants, which are used to predict physical, chemical and pharmacological properties of organic molecules, can be recovered from it. In this article we give the general closed form of the Hosoya polynomial of the generalized Möbius ladder $M(m,n)$ for arbitrary $m$ and for $n=3$. Moreover, we recover Wiener, hyper Wiener, Tratch-Stankevitch-Zefirov, and Harary indices from it.
The $M$-polynomial was introduced by Deutsch and Klavžar in 2015 as a graph polynomial to provide an easy way to find closed formulas of degree-based topological indices, which are used to predict physical, chemical, and pharmacological properties of organic molecules. In this paper we give general closed forms of the $M$-polynomial of the generalized Möbius ladder and its line graph. We also compute Zagreb Indices, generalized Randić indices, and symmetric division index of these graphs via the $M$-polynomial.
In this paper we introduce generalized Möbius ladder $M_{m,n}$ and give its metric dimension. Moreover, it is observed that, depending on even and odd values of $m$ and $n$, it has two subfamilies with constant metric dimensions.
Using a simple recurrence relation we give a new method to compute Jones polynomials of closed braids: we find a general expansion formula and a rational generating function for Jones polynomials. The method is used to estimate degree of Jones polynomials for some families of braids and to obtain general qualitative results.
Double Fibonacci sequences are introduced and they are related to operations with Fibonacci modules. Generalizations and examples are also discussed.