A topological descriptor is regarded as a numerical parameter derived by using mathematical tools from the molecular graph of different chemical structures. The chemical graph theory is a paramount section of mathematical chemistry. In this section, there are many topological parameters, that have very useful characteristics to study the molecular structure of chemicals. In this article, we investigate topological indices of concealed non-kekulean benzenoid hydrocarbon graph. We will compute general Randic index, general sum connectivity index, sum connectivity index, general version of harmonic index, harmonic index, first, second and third Zagreb indices, SK, SK₁, SK₂ indices, augmented Zagreb index, atomic bond connectivity index, geometric arithmetic index, first and second gourava indices, first and second hyper-gourava indices and 4th version of atomic bond connectivity, 5th version of geometric arithmetic index, and the Sanskurti index.

In the chemical industry, topological indices play an important role in defining the properties of chemical compounds. They are numerical parameters and structure invariant. It is a proven fact by scientists that topological properties are influential tools for interconnection networks. In this paper, we will use stellation, medial and bounded dual operations to build transformed networks from zigzag and triangular benzenoid structures. Using M-polynomial, we compute the first and second Zagreb indices, second modified Zagreb indices, symmetric division index, general Randic index, reciprocal general Randic index. We also calculate atomic bond connectivity index, geometric arithmetic index, harmonic index, first and second Gourava indices, first and second hyper Gourava indices.

Graph theory has great deal of application in disciplines like biology, computer science, informatics, engineering, mathematics, social science, linguistics and medicine. Topological indices are created by labeling the chemical structure through numerical parameters. These notations link chemical compounds physicochemical features such as boiling temperature, stability, strain energy etc, to its molecular structure. Different topological features of chemical structure have been explored. One of the molecular graphs topological indices are the connection indices defined on the number of connection between vertices of distance two. In this work, we compute the first Zagreb connection index, second Zagreb connection index, and modified first Zagreb connection index for hexagonal network and non kekulean benzenoid hydrocarbon.

A topological index is a numerical character associated with a graph that is invariant under graph isomorphism and describe the graphs topology. There are several graph operations that may be used to change it into a new structure, such as constructing a stellation, bounded dual, complement, subdivided, line graph, minor, dual, and medial. In this paper, we construct transformed networks from the concealled non-kekulean benzenoid hydrocarbon structure by applying stellation and bounded dual operations, further we study their degree based topological properties by appropriately labeling the graph. Degree based topological indices are playing significant role among other types of indices in chemical, pharmaceutical and bio-informatics industry, since they correlate the structure with its physicochemical properties.