The forgotten topological index of a molecular graph $G$ is defined as $F(G)=sum_{vin V(G)}d^{3}(v)$, where $d(u)$ denotes the degree of vertex $u$ in $G$. The first through the sixth smallest forgotten indices among all trees, the first through the third smallest forgotten indices among all connected graph with cyclomatic number $gamma=1,2$, the first through<br /...

We describe some necessary conditions for the existence of a Hamiltonian path in any graph (in other words, for a graph to be traceable). These conditions result in a linear time algorithm to decide the Hamiltonian path problem for cactus graphs. We apply this algorithm to several molecular databases to report the numbers of graphs that are traceable cactus graphs.

Chemical compounds and drugs are often modelled as graphs (for example, Polyhex Nanotubes and Dendrimer Nanostar) where each vertex represents an atom of molecule and covalent bounds between atoms are represented by edges between the corresponding vertices. This graph derived from a chemical compounds is often called its molecular graph and can be different structures. The edge Wiener index of ...

The generalized hierarchical product of graphs was introduced by L. Barriére et al in 2009. In this paper, reformulated first Zagreb index of generalized hierarchical product of two connected graphs and hence as a special case cluster product of graphs are obtained. Finally using the derived results the reformulated first Zagreb index of some chemically important graphs such as square comb latt...

For molecular weights up to 150, all molecular graphs corresponding to possible organic compounds made of C,H,N,O were generated using the structure generator MOLGEN. The numbers obtained were compared to the numbers of molecular graphs corresponding to actually known compounds as retrieved from the Beilstein file. The results suggest that the overwhelming majority of all organic compounds (eve...

Procuring expressive molecular representations underpins AI-driven molecule design and scientific discovery. The research mainly focuses on atom-level homogeneous graphs, ignoring the rich information in subgraphs or motifs. However, it has been widely accepted that substructures play a dominant role identifying determining properties. To address such issues, we formulate heterogeneous graphs (...