ThreeTopological Indices of TwoNewVariants ofGraphProducts (original) (raw)

Further Results on Topological Indices of Two Corona Variants of Graph Products

arXiv (Cornell University), 2021

Graph operations are crucial for building complicated network architectures from simple graphs. In [7], authors defined two new variants of Corona product and investigated their some topological indices. In this paper, we extended the work and found the formulas of forgotten, first hyper Zagreb, and reduced second Zagreb indices for Corona join product and subdivision vertex join products of graphs.

Zagreb Indices of Double Join and Double Corona of Graphs Based on the Total Graph

International Journal of Applied and Computational Mathematics

The Zagreb indices for a graph are defined as sum of the square of the degrees of all the vertices of the graph and sum of the product of degrees of all the pair of adjacent vertices of that graph. In this study, the Zagreb indices of two recently introduced graph operations, called double join of graphs based on the total graph and double corona of graphs based on the total graph are computed in terms of different topological indices of their factor graphs and hence some application of the derived results are also discussed. Keywords Zagreb indices • Double join of graphs based on the total graph • Double corona of graphs based on the total graph

Degree-Based Topological Indices of Generalized Subdivision Double-Corona Product

Journal of Chemistry, 2022

Graph operations play an important role in constructing complex network structures from simple graphs. Computation of topological indices of these complex structures via graph products is an important task. In this paper, we generalized the concept of subdivision double-corona product of graphs and investigated the exact expressions of the first and second Zagreb indices, first reformulated Zagreb index, and forgotten topological index (F-index) of this graph operation.

Topological Indices of Some New Graph Operations

A chemical graph theory is a fascinating branch of graph theory which has many applications related to chemistry. A topological index is a real number related to a graph, as its considered a structural invariant. It's found that there is a strong correlation between the properties of chemical compounds and their topological indices. In this paper, we introduce some new graph operations for the first Zagreb index, second Zagreb index and forgotten index "F-index". Furthermore, it was found some possible applications on some new graph operations such as roperties of molecular graphs that resulted by alkanes or cyclic alkanes.

Topological Indices of Some New Graph Operations and Their Possible Applications

2021

A chemical graph theory is a fascinating branch of graph theory which has many applications related to chemistry. A topological index is a real number related to a graph, as its considered a structural invariant. It’s found that there is a strong correlation between the properties of chemical compounds and their topological indices. In this paper, we introduce some new graph operations for the first Zagreb index, second Zagreb index and forgotten index ”F-index”. Furthermore, it was found some possible applications on some new graph operations such as roperties of molecular graphs that resulted by alkanes or cyclic alkanes.

Mapping Connectivity Patterns: Degree-Based Topological Indices of Corona Product Graphs

Journal of Applied Mathematics

Graph theory (GT) is a mathematical field that involves the study of graphs or diagrams that contain points and lines to represent the representation of mathematical truth in a diagrammatic format. From simple graphs, complex network architectures can be built using graph operations. Topological indices (TI) are graph invariants that correlate the physicochemical and interesting properties of different graphs. TI deal with many properties of molecular structure as well. It is important to compute the TI of complex structures. The corona product (CP) of two graphs G and H gives us a new graph obtained by taking one copy of G and V G copies of H and joining the i th vertex of G to every vertex in the i th copy of H . In this paper, based on various CP graphs composed of paths, cycles, and complete graphs, the geometric index (GA) and atom bond connectivity (ABC) index are investigated. Particularly, we discussed the corona products P s ⨀ P t , C t ⨀ C s , K t ⊙ K s , K t ⊙ P s , and...

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.

First General Zagreb Co-Index of Graphs under Operations

Journal of Mathematics

Topological indices are graph-theoretic parameters which are widely used in the subject of chemistry and computer science to predict the various chemical and structural properties of the graphs respectively. Let G be a graph; then, by performing subdivision-related operations S , Q , R , and T on G , the four new graphs S G (subdivision graph), Q G (edge-semitotal), R G (vertex-semitotal), and T G (total graph) are obtained, respectively. Furthermore, for two simple connected graphs G and H , we define F -sum graphs (denoted by G + F H ) which are obtained by Cartesian product of F G and H , where F ∈ S , R , Q , T . In this study, we determine first general Zagreb co-index of graphs under operations in the form of Zagreb indices and co-indices of their basic graphs.

Topological Indices of Families of Bistar and Corona Product of Graphs

Journal of Mathematics, 2022

Topological indices are graph invariants that are used to correlate the physicochemical properties of a chemical compound with its (molecular) graph. In this study, we study certain degree-based topological indices such as Randić index, Zagreb indices, multiplicative Zagreb indices, Narumi-Katayama index, atom-bond connectivity index, augmented Zagreb index, geometricarithmetic index, harmonic index, and sum-connectivity index for the bistar graphs and the corona product K m oK n ′ , where K n ′ represents the complement of complete graph K n .

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.