On the Computation of Some Topological Descriptors to Find Closed Formulas for Certain Chemical Graphs

In this research paper, we will compute the topological indices (degree based) such as the ordinary generalized geometric-arithmetic (OGA) index, first and second Gourava indices, first and second hyper-Gourava indices, general Randic´ index R γ G , for γ = ± 1 , ± 1 / 2 , harmonic index, general version of the harmonic index, atom-bond connectivity (ABC) index, SK, SK1, and SK2 indices, sum-connectivity index, general sum-connectivity index, and first general Zagreb and forgotten topological indices for various types of chemical networks such as the subdivided polythiophene network, subdivided hexagonal network, subdivided backbone DNA network, and subdivided honeycomb network. The discussion on the aforementioned networks will give us very remarkable results by using the aforementioned topological indices.

Some valency oriented molecular invariants of certain networks.

Background: The valency of an atom in a molecular structure is the number of its neighboring atoms. A large number of valency based molecular invariants have been conceived, which correlate certain physio-chemical properties like boiling point, stability, strain energy and many more of chemical compounds. Objective: Our aim is to study the valency based molecular invariants for four hexa chemical structures, namely hexagonal network, honeycomb network, oxide network and silicate sheet network. Method: We use the technique of atom-bonds partition according to the valences of atoms to find results. Results: Exact values of valency-based molecular invariants, namely the Randić index, atom bond connectivity index, geometric arithmetic index, harmonic index, Zagreb indices, Zagreb polynomials, F-index and F-polynomial are found for four hexa chemical structures.

Nilai Total Ketakteraturan Titik dari Honeycomb Network

Topik penelitian ini adalah pelabelan total tak teratur titik pada honeycomb network. Misalkan adalah suatu graf, fungsi disebut pelabelan- total tak teratur titik (vertex irregular total -labeling) pada , jika setiap dua titik yang berbeda di mempunyai bobot yang berbeda. Bobot titik di terhadap fungsi adalah . Bilangan bulat positif terkecil sedemikian sehingga mempunyai suatu pelabelan- total tak teratur titik dinamakan nilai total ketakteraturan titik (total vertex irregularity strength) dari , dilambangkan dengan . Dari hasil penelitian ini diperoleh nilai total ketakteraturan titik dari honeycomb network yang dinotasikan dengan untuk adalah .

Tight Bounds on 1-Harmonious Coloring of Certain Graphs

Graph coloring is one of the most studied problems in graph theory due to its important applications in task scheduling and pattern recognition. The main aim of the problem is to assign colors to the elements of a graph such as vertices and/or edges subject to certain constraints. The 1-harmonious coloring is a kind of vertex coloring such that the color pairs of end vertices of every edge are different only for adjacent edges and the optimal constraint that the least number of colors is to be used. In this paper, we investigate the graphs in which we attain the sharp bound on 1-harmonious coloring. Our investigation consists of a collection of basic graphs like a complete graph, wheel, star, tree, fan, and interconnection networks such as a mesh-derived network, generalized honeycomb network, complete multipartite graph, butterfly, and Benes networks. We also give a systematic and elegant way of coloring for these structures.

Analysis of the low-temperature restoration process of graphene oxide based on in situ conductivity measurement

Graphene, a honeycomb network of sp2 carbon atoms, is expected to replace conventional materials in various fields, which makes it important to develop a high-throughput graphene synthesis method for industrial applications.