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. (doi: 10.5562/cca2294) Keywords: topological index, molecular structure descriptor, vertex-degree-based topological index, molecular graph, chemical graph theory
The correlation ability of 20 vertex-degree-based topological indices,
occurring in the chemical literature, is tested for the case of standard
heats of formation and normal boiling points of octane ...isomers. It is found
that the correlation ability of many of these indices is either rather weak
or nil. The augmented Zagreb index and the atom-bond connectivity index yield
the best results.
•Determine the maximal values of the number of inlets over f-benzenoids with the number of internal vertices ni=1;2;3;4,respectively.•Get the minimal values of the number of hexagons over ...f-benzenoids when the order n≡0;1;2;3(mod4),respectively.•Give the extremal values of some well-known VTsover the set of fbenzenoids with a given order.•Characterize the extremal fbenzenoids attaining these values.
In the theoretical chemistry, pharmacology and biology literature, numerous VDB topological indices were introduced to predict physio-chemical properties of chemical compounds. As a kind of polycyclic aromatic hydrocarbons, f–benzenoids are abundant in real substances such as coal tar, etc. It is valuable to study the attributes of f–benzenoids by virtue of topological indices. The main dedication of this paper is to obtain extremal values for VDB topological indices of f–benzenoids with a given order. Furthermore, the extremal f–benzenoids attaining these values are also characterized.
Graph theory is attracting much attention due to the use of devices like topological indices. A topological graph index is defined according to a certain rule. After defining a new topological index, ...it must be checked for a possible correlation with the properties of a particular chemical substance along with a few mathematical properties. As most of the indices involve some data related to the degrees of the vertices, types of edges, and various details of the chemical compound under the study, it is very useful in chemistry applications. The applications include drug design, modeling of a compound, the study of structure relationships, etc. In this work, the redefined Zagreb indices, ABC index, GA index, Augmented Zagreb index, neighborhood version of redefined Zagreb indices, ABC4 index, GA5 index, and Sanskruti index is computed for the chemical compound called porous graphene. The work is concluded with a detailed conclusion of the study considered.
Molecules can be modelled by graphs to obtain their required properties by means of only mathematical methods and formulae. In this paper, several degree-based graph indices of one of the important ...chemical compounds called as polyester are calculated to determine several chemical and physicochemical properties of polyester.
•Four topological indices based on k-eccentricity were introduced. The algorithms on these topological indices were devised. The time complexity was analyzed.•we employ the given topological indices ...based on 2- and 3-eccentricity as the feature vectors to predict anti-HIV activity by devising machine learning predicting models with the help of Support Vector Machine, K Nearest Neighbor and Decision Tree, respectively.•Through these experiments, we find that these topological indices based on the k-eccentricity (k=2,3) have good applications in predicting anti-HIV activity. The highest predicting accuracy is 99.7%, while the lowest is 97.7%.
As molecular descriptors, topological indices based on k-eccentricity of a graph are introduced. Firstly we devise an algorithm for these indices based on 3-eccentricity and analyze the computing complexity. As their applications, we employ the topological indcies based on 2- and 3-eccentricity as the feature vectors to predict anti-HIV activity by devising machine learning predicting models with the help of Support Vector Machine (SVM), K Nearest Neighbor (KNN) and Decision Tree (DecTree), respectively. Experiment results show that the highest accuracy is 99.7%, while the lowest is 97.7% except the special cases. The special cases are that the experiments are with the single 2-CEI or 3-CEI as the feature vector, respectively. Through these experiments, we find that these topological indices based on the k-eccentricity (k=2,3) have good applications in predicting anti-HIV activity. But not every feature vector is generally applicable. Different feature vectors may be used to different models. Furthermore, there is no clear relationship between the dimension of feature vectors and the accuracy of prediction.
In this paper, we determine some degree-based topological indices, such as the Sombor index, the first and second Zagreb indices, the forgotten topological index, the Narumi–Katayama index, the first ...and second multiplicative Zagreb indices, the atom-bond connectivity index, and eccentricity-based topological indices such as total eccentricity, the first and second Zagreb eccentricity indices, and the eccentricity connectivity index of the zero divisor graph with vertex set non-zero zero divisors of the reduced ring of the direct product of three finite fields.
Molecular topological indices are numerical descriptor of molecular structure obtained via molecular graph G. The forgotten topological index F(G) is a vertex degree based topological index and it ...can be expressed with
where d(u) denotes the degree of u. The forgotten co-index Co-F(G) is defined as the sum of squares of a graph's vertex degrees which is not adjacent. In this study, the F(G) and Co-F(G) index of HAC
5
C
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, HAC
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, linear n-phenylenes and cyclic phenylenes nanostructures are computed for possible works in the properties of molecules such as structure-property relationship. In addition, polynomials of the forgotten index and co-index are found for these nanostructures.
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