Topological indices are numerical numbers assigned to the graph/structure and are useful to predict certain physical/chemical properties. In this paper, we give explicit expressions of novel Banhatti indices, namely, first K Banhatti index B 1 G , second K Banhatti index B 2 G , first K hyper-Banhatti index HB 1 G , second K hyper-Banhatti index HB 2 G , and K Banhatti harmonic index H b G for hyaluronic acid curcumin and hydroxychloroquine. The multiplicative version of these indices is also computed for these structures.
Let G be a simple graph with vertex set V G and edge set E G . An edge labeling δ : E G ⟶ 0,1 , … , p − 1 , where p is an integer, 1 ≤ p ≤ E G , induces a vertex labeling δ ∗ : V H ⟶ 0,1 , … , p − 1 defined by δ ∗ v = δ e 1 δ e 2 ⋅ δ e n mod p , where e 1 , e 2 , … , e n are edges incident to v . The labeling δ is said to be p -total edge product cordial (TEPC) labeling of G if e δ i + v δ ∗ i − e δ j + v δ ∗ j ≤ 1 for every i , j , 0 ≤ i ≤ j ≤ p − 1 , where e δ i and v δ ∗ i are numbers of edges and vertices labeled with integer i , respectively. In this paper, we have proved that the stellation of square grid graph admits a 3-total edge product cordial labeling.
Sierpinski graphs are a widely observed family of fractal-type graphs relevant to topology, Hanoi Tower mathematics, computer engineering, and around. Chemical implementations of graph theory establish significant properties, such as chemical activity, physicochemical properties, thermodynamic properties, and pharmacological activities of a molecular graph. Specific graph descriptors alluded to as topological indices are helpful to predict these properties. These graph descriptors have played a key role in quantitative structure-property/structure-activity relationships (QSPR/QSAR) research. The objective of this article is to compute Randic index ( R − 1 / 2 ), Zagreb index M 1 , sum-connectivity index SCI , geometric-arithmetic index GA , and atom-bond connectivity ABC index based on ev-degree and ve-degree for the Sierpinski networks S n , m .
Vanadium is a biologically active product with significant industrial and biological applications. Vanadium is found in a variety of minerals and fossil fuels, the most common of which are sandstones, crude oil, and coal. Topological descriptors are numerical numbers assigned to the molecular structures and have the ability to predict certain of their physical/chemical properties. In this paper, we have studied topological descriptors of vanadium carbide structure based on ev and ve degrees. In particular, we have computed the closed forms of Zagreb, Randic, geometric-arithmetic, and atom-bond connectivity (ABC) indices of vanadium carbide structure based on ev and ve degrees. This kind of study may be useful for understanding the biological and chemical behavior of the structure.
The concept of H-bases, introduced long ago by Macauly, has become an important ingredient for the treatment of various problems in computational algebra. The concept of H-bases is for ideals in polynomial rings, which allows an investigation of multivariate polynomial spaces degree by degree. Similarly, we have the analogue of H-bases for subalgebras, termed as SH-bases. In this paper, we present an analogue of H-bases for finitely generated ideals in a given subalgebra of a polynomial ring, and we call them “HSG-bases.” We present their connection to the SAGBI-Gröbner basis concept, characterize HSG-basis, and show how to construct them.
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