In this article, we calculate various topological invariants such as symmetric division degree index, redefined Zagreb VL first and second exponential multiplicative indices, entropy, entropies, entropy. We take the chemical compound named Proanthocyanidins, which is a very useful polyphenol in human’s diet. They are beneficial for one’s health. These compounds extracted from grape seeds. treme...

A topological index of a graph is a numeric quantity related to a structure of a molecule which is invariant under graph automorphism. Recently, Ghorbani and Hosseinzadeh introduced Fourth Zagreb index of graphs. In this paper we determine a closed formula of this new topological index of the famous Benzenoid family named Circumcoronene series of Benzenoid Hk.

The matrix representations of hypergraphs have been defined via hypermatrices initially. In recent studies, the Laplacian hypergraphs, a generalization matrix, has introduced. this article, based on definition, we derive bounds depending pair-degree, maximum degree, and first Zagreb index for greatest eigenvalue energy r-uniform regular hypergraphs. As result these bounds, Nordhaus–Gaddum type ...

Using graph-theoretical techniques, we establish an inequality regarding the number of walks and closed walks in a graph. This inequality yields several upper bounds for the number of closed walks in a graph in terms of the number of vertices, number of edges, maximum degree, degree sequence, and the Zagreb indices of the graph. As applications, we also present some new upper bounds on the Estr...