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Journal ArticleDOI

Neighbourhood degree-based topological indices of graphene structure

Kalyani Desikan1
01 Jan 2021-Vol. 11, Iss: 5, pp 13681-13694

AboutThe article was published on 2021-01-01 and is currently open access. It has received None citation(s) till now. The article focuses on the topic(s): Neighbourhood (mathematics).

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Journal ArticleDOI
TL;DR: A critical review of the synthesis methods for graphene and its derivatives as well as their properties and the advantages of graphene-based composites in applications such as the Li-ion batteries, supercapacitors, fuel cells, photovoltaic devices, photocatalysis, and Raman enhancement are described.
Abstract: Graphene has attracted tremendous research interest in recent years, owing to its exceptional properties. The scaled-up and reliable production of graphene derivatives, such as graphene oxide (GO) and reduced graphene oxide (rGO), offers a wide range of possibilities to synthesize graphene-based functional materials for various applications. This critical review presents and discusses the current development of graphene-based composites. After introduction of the synthesis methods for graphene and its derivatives as well as their properties, we focus on the description of various methods to synthesize graphene-based composites, especially those with functional polymers and inorganic nanostructures. Particular emphasis is placed on strategies for the optimization of composite properties. Lastly, the advantages of graphene-based composites in applications such as the Li-ion batteries, supercapacitors, fuel cells, photovoltaic devices, photocatalysis, as well as Raman enhancement are described (279 references).

3,012 citations

Journal ArticleDOI
Abstract: The degree of a vertex of a molecular graph is the number of first neighbors of this vertex. A large number of molecular-graph-based structure descriptors (topological indices) have been conceived, depending on vertex degrees. We summarize their main properties, and provide a critical comparative study thereof.

379 citations

Book
01 Jan 2012

141 citations

Journal ArticleDOI
Abstract: Let $G$ be a graph and let $m_{ij}(G)$, $i,jge 1$, be the number of edges $uv$ of $G$ such that ${d_v(G), d_u(G)} = {i,j}$. The {em $M$-polynomial} of $G$ is introduced with $displaystyle{M(G;x,y) = sum_{ile j} m_{ij}(G)x^iy^j}$. It is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular case to the single problem of determining the $M$-polynomial. The new approach is also illustrated with examples.

57 citations

Journal ArticleDOI
Abstract: A molecular network can be characterized by several different ways, like a matrix, a polynomial, a drawing or a topological descriptor. A topological descriptor is a numeric quantity associated with a network or a graph that characterizes its whole structural properties. Analyzing and determining the topological indices and structural properties of a network or a graph have been a worthy studied topic in the field of chemistry, networks analysis, etc. In this paper, we consider several types of the generalized Sierpinski networks and investigate the explicit expressions of some well-known valency-based topological indices. Taking into account the other structural property of the generalized Sierpinski networks, the average degree is determined.

52 citations