The application of graph theory in chemical and molecular structure research far exceeds people's expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonded by edges. In this report, we study the silicon-carbon Si₂C₃-I[p,q] and Si₂C₃-II[p,q]. We compute several Zagreb polynomials and Redefined Zagreb indices of these silicon-carbons.

The topological index is a numerical quantity based on the characteristics of various invariants or molecular graph. For ease of discussion, these indices are classified according to their logical derivation from topological invariants rather than their temporal development. Degree based topological indices depends upon the degree of vertices. This paper computes Zagreb polynomials and redefined first, second and third Zagrebindices of Bismuth Tri-Iodide chains and sheets.

Topological indices have important role in theoretical chemistry for QSPR researches. Among the all topological indices the Randić and the Zagreb indices have been used more considerably than any other topological indices in chemical and mathematical literature. Most of the topological indices as in the Randić and the Zagreb indices are based on the degrees of the vertices of a connected graph. Recently novel two degree concepts have been defined in graph theory; ev-degrees and ve-degrees. In this study we define ev-degree Zagreb index, ve-degree Zagreb indices and ve-degree Randić index by using these new graph invariants as parallel to their corresponding classical degree versions. We compare these new group ev-degree and ve-degree indices with the other well-known and most used topological indices in literature such as; Wiener, Zagreb and Randić indices by modelling some physicochemical properties of octane isomers. We show that the ev-degree Zagreb index, the ve-degree Zagreb and the ve-degree Randić indices give better correlation than Wiener, Zagreb and Randić indices to predict the some specific physicochemical properties of octanes. We investigate the relations between the second Zagreb index and ev-degree and ve-degree Zagreb indices and some mathematical properties of ev-degree and ve-degree Zagreb indices.

M-polynomial of different molecular structures helps to calculate many topological indices. A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR) quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Zagreb indices, Randic index, Symmetric division index, Harmonic index, Inverse sum index, Augmented Zagreb index, multiple Zagreb indices etc. are correlated. In this report, we compute closed forms of M-polynomial, first Zagreb polynomial and second Zagreb polynomial of Octagonal network. From the M-polynomial we recover some degree-based topological indices for Octagonal network. Moreover, we give a graphical representation of our results.

Morphometric analysis of Holocene pebbles from the Sava River gravels, in Zagreb alluvial aquifer system (NW Croatia), revealed distribution of their shapes along 30 km long observed watercourse. Limestones, dolomites and sandstones are determined as major (> 4%), and effusive magmatics, cherts and tuffs as minor lithotypes of the pebbles (up to 4%). Their distributions indicate mainly distant Alpine provenance for carbonate (limestones and dolomites) pebbles and local input for sandstones and minor lithotypes, laterally from the Samoborska gora and Medvednica Mts. Carbonates have predominately disc and sphere shapes, implying also their mainly distant sources. Scattered distributions of pebble shapes (sphere, disc, blade and rod) for sandstones and minor lithotypes indicate multiple sources, some of them probably local. Original sedimentary environments for main pebble lithotypes are tentatively interpreted from their flatness ratios, indicating predominant lake shore environments, followed by moraine and riverbed.

We characterize the form of the order divisor graph of cyclic groups based on the group order. Furthermore, we describe some topological indices of the order divisor graph of cyclic groups, including the Wiener index, Harary index, first Zagreb index, and second Zagreb index.

Graph theory plays a crucial role in modeling and designing of chemical structure or chemical network. Chemical Graph theory helps to understand the molecular structure of molecular graph. The molecular graph consists of atoms as vertices and bonds as edges. Topological indices capture symmetry of molecular structures and give it a mathematical language to predict properties such as boiling points, viscosity, the radius of gyrations etc. In this article, we study the chemical graph of carbon Crystal structure of graphite and cubic carbon and compute several degree-based topological indices. Firstly we compute M-Polynomials of these structures and then from these M-polynomials we recover nine degree-based topological indices.

The study was performed to get the first insight of distribution of the low field volume magnetic susceptibility (MS) throughout the Zagreb city area, based on in-situ field measurements. Most interesting locations were selected for soil sampling and geochemical content was determined using ICP-OES. A geostatistical approach was applied on MS and geochemical results. Median value of 0.245 x 10-3 SI units is proposed to be used as relevant average MS value in Zagreb area. Mean concentrations of heavy metals in Zagreb soils (in µg/g) are: Pb (36.82), Zn (87.77), Cu (30.84), Cd (0.66), Cr (29.04), Co (11.89) and Ni (28.40), being relatively low in comparison with Croatian legislation and with European and world average. Boxplot analyses showed that 45% of studied elements do not show any anomaly, while the rest of elements mostly show only one weak anomaly and they are located at the same sites as MS anomalies. Statistical analysis found significant correlations between MS and following elements: Cd, Co, Fe, Mn, Na, Pb, Sb and Zn. In-situ MS measurements proved to be an efficient tool for initial screening of large areas in terms of elevated heavy elements concentrations, enabling cheap and fast assessment of state of environment.

The topological index is a numerical quantity based on the characteristics of various invariants or molecular graph. For ease of discussion, these indices are classified according to their logical derivation from topological invariants rather than their temporal development. Degree based topological indices depends upon the degree of vertices. This paper computes degree based topological indices of Bismuth Tri-Iodide chains and sheets with the help of M-polynomial.

Titania is one of the most comprehensively studied nanostructures due to its widespread applications in production of catalytic, gas- sensing and corrosion- resistance materials [1]. M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices which are numerical parameters capturing structural and chemical properties. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules are correlated with their structure like boiling point, stability, strain energy etc of chemical compounds. In this paper, we determine M-polynomials of single-walled titanium (SW TiO2) nanotubes and recover important topological degree based indices of them to theoretically judge these nanotubes. We also use Maple to plot surfaces associated to different types of single-walled titanium (SW TiO2) nanotubes.