Degree Based Weighted Entropy Indices of Hyaluronic Acid-Curcumin Conjugates: an Anti-Tumor Drug

Computing degree based topological indices of algebraic hypergraphs

Topological indices are numerical parameters that indicate the topology of graphs or hypergraphs. A hypergraph H = ( V ( H ) , E ( H ) ) consists of a vertex set V ( H ) and an edge set E ( H ) , where each edge e ∈ E ( H ) is a subset of V ( H ) with at least two elements. In this paper, our main aim is to introduce a general hypergraph structure for the prime ideal sum (PIS)- graph of a commutative ring. The prime ideal sum hypergraph of a ring R is a hypergraph whose vertices are all non-trivial ideals of R and a subset of verticesE i with at least two elements is a hyperedge whenever I + J is a prime ideal of R for each non-trivial ideal I, J inE i andE i is maximal with respect to this property. Moreover, we also compute some degree-based topological indices (first and second Zagreb indices, forgotten topological index, harmonic index, Randić index, Sombor index) for these hypergraphs. In particular, we describe some degree-based topological indices for the newly defined algebraic hypergraph based on prime ideal sum forZ n where n = p α , p q , p 2 q , p 2 q 2 , p q r , p 3 q ,p 2 q r , p q r s for the distinct primes p , q , r and s.

Reduced reverse degree-based topological indices of graphyne and graphdiyne nanoribbons with applications in chemical analysis

Graphyne and Graphdiyne Nanoribbons reveal significant prospective with diverse applications. In electronics, they propose unique electronic properties for high-performance nanoscale devices, while in catalysis, their excellent surface area and reactivity sort them valuable catalyst supports for numerous chemical reactions, contributing to progresses in sustainable energy and environmental remediation. The topological indices (TIs) are numerical invariants that provide important information about the molecular topology of a given molecular graph. These indices are essential in QSAR/QSPR analysis and play a significant role in predicting various physico-chemical characteristics. In this article, we present a formula for computing reduced reverse (RR) degree-based topological indices for graphyne and graphdiyne nanoribbons, including the RR Zagreb indices, RR hyper-Zagreb indices, RR forgotten index, RR atom bond connectivity index, and RR Geometric-arithmetic index. We also execute a graph-theoretical analysis and comparison to demonstrate the critical significance and validate the acquired results. Our findings provide insights into the structural and chemical properties of these nanoribbons and contribute to the development of new materials for various applications.