On Graph Invariants of Oxide Network (original) (raw)

THE SECOND HYPER-ZAGREB INDEX OF GRAPH OPERATIONS

A graph can be recognized by numeric number, polynomial or matrix which represent the whole graph. Topological index is a numerical descriptor of a molecule, based on a certain topological feature of the corresponding molecular graph, it is found that there is a strong correlation between the properties of chemical compounds and their molecular structure. Zagreb indices are numeric numbers related to graphs. In this study, the second Hyper-Zagreb index for some special graphs, and graph operations has been computed, that have been applied to compute the second Hyper-Zagreb index for Nano-tube and Nano-torus.

Zagreb Indices of a New Sum of Graphs

Ural Mathematical Journal

The first and second Zagreb indices, since its inception have been subjected to an extensive research in the physio- chemical analysis of compounds. In [6] Hanyuan Deng et.al computed the first and second Zagreb indices of four new operations on a graph defined by M. Eliasi, B. Taeri in [4]. Motivated from this we define a new operation on graphs and compute the first and second Zagreb indices of the resultant graph. We illustrate the results with some examples.

On General Reduced Second Zagreb Index of Graphs

Mathematics

Graph-based molecular structure descriptors (often called “topological indices”) are useful for modeling the physical and chemical properties of molecules, designing pharmacologically active compounds, detecting environmentally hazardous substances, etc. The graph invariant GRMα, known under the name general reduced second Zagreb index, is defined as GRMα(Γ)=∑uv∈E(Γ)(dΓ(u)+α)(dΓ(v)+α), where dΓ(v) is the degree of the vertex v of the graph Γ and α is any real number. In this paper, among all trees of order n, and all unicyclic graphs of order n with girth g, we characterize the extremal graphs with respect to GRMα(α≥−12). Using the extremal unicyclic graphs, we obtain a lower bound on GRMα(Γ) of graphs in terms of order n with k cut edges, and completely determine the corresponding extremal graphs. Moreover, we obtain several upper bounds on GRMα of different classes of graphs in terms of order n, size m, independence number γ, chromatic number k, etc. In particular, we present an u...

The multiplicative Zagreb indices of graph operations

Journal of Inequalities and Applications, 2013

Recently, Todeschini et al. (Novel Molecular Structure Descriptors -Theory and Applications I, pp. 73-100, 2010), Todeschini and Consonni (MATCH Commun. Math. Comput. Chem. 64:359-372, 2010) have proposed the multiplicative variants of ordinary Zagreb indices, which are defined as follows: These two graph invariants are called multiplicative Zagreb indices by Gutman (Bull. Soc. Math. Banja Luka 18:17-23, 2011). In this paper the upper bounds on the multiplicative Zagreb indices of the join, Cartesian product, corona product, composition and disjunction of graphs are derived and the indices are evaluated for some well-known graphs. MSC: 05C05; 05C90; 05C07

The general Zagreb index of lattice networks

2019

A topological index is a real number which is derived from a network or a graph by mathematically that characterizes the whole of its structural properties. Recently, there are various topological indices that have been introduced in mathematical chemistry to predict the properties of molecular topology. Among, the degree based topological indices such as Zagreb indices, forgotten topological index, redefined Zagreb index, Randic index, general first Zagreb index, symmetric division deg index and hence so forth are most important, because of their chemical significance. In this work, we study the general Zagreb index of hexagonal and triangular lattice networks.

Reformulated Zagreb Indices of Some Derived Graphs

Mathematics

A topological index is a numeric quantity that is closely related to the chemical constitution to establish the correlation of its chemical structure with chemical reactivity or physical properties. Miličević reformulated the original Zagreb indices in 2004, replacing vertex degrees by edge degrees. In this paper, we established the expressions for the reformulated Zagreb indices of some derived graphs such as a complement, line graph, subdivision graph, edge-semitotal graph, vertex-semitotal graph, total graph, and paraline graph of a graph.

On the Reformulated Second Zagreb Index of Graph Operations

Journal of Chemistry, 2021

Topological indices (TIs) are expressed by constant real numbers that reveal the structure of the graphs in QSAR/QSPR investigation. The reformulated second Zagreb index (RSZI) is such a novel TI having good correlations with various physical attributes, chemical reactivities, or biological activities/properties. The RSZI is defined as the sum of products of edge degrees of the adjacent edges, where the edge degree of an edge is taken to be the sum of vertex degrees of two end vertices of that edge with minus 2. In this study, the behaviour of RSZI under graph operations containing Cartesian product, join, composition, and corona product of two graphs has been established. We have also applied these results to compute RSZI for some important classes of molecular graphs and nanostructures.

The Generalized Zagreb Index of Some Carbon Structures

Acta Chemica Iasi

In chemical graph theory, chemical structures are model edthrough a graph where atoms are considered as vertices and edges are bonds between them. In chemical sciences, topological indices are used for understanding the physicochemical properties of molecules. In this work, we study the generalized Zagreb index for three types of carbon allotrope’s theoretically.

Some formulae for the Zagreb indices of graphs

2012

In this study, we first find formulae for the first and second Zagreb indices and coindices of certain classical graph types including path, cycle, star and complete graphs. Secondly we give similar formulae for the first and second Zagreb coindices.