Weighted Mostar invariants of chemical compounds: An analysis of structural stability.

The concept of the weighted Mostar invariant is a mathematical tool used in chemical graph theory to study the stability of chemical compounds. Several recent studies have explored the weighted Mostar invariant of various chemical structures, including hydrocarbons, alcohols, and other organic compounds. One of the key advantages of the weighted Mostar invariant is that it can be easily computed for large and complex chemical structures, making it a valuable tool for studying the stability of a wide range of chemical compounds. This notion has been utilized to build novel approaches for forecasting chemical compound stability, such as machine learning algorithms. The focus of the paper is to demonstrate the weighted Mostar indices of three specific nanostructures: silicon dioxide (SIO2, poly-methyl methacrylate network (PMMA(s)), and melem chains (MC(h)). The authors seek to provide the findings of their investigation of these nanostructures using the weighted Mostar invariant.

The Wiener index, degree distance index and Gutman index of composite hypergraphs and sunflower hypergraphs.

Topological invariants are numerical parameters of graphs or hypergraphs that indicate its topology and are known as graph or hypergraph invariants. In this paper, topological indices of hypergraphs such as Wiener index, degree distance index and Gutman index are considered. A g-composite hypergraphs is a hypergraphs that is obtained by the union of g hypergraphs with every hypergraph has exactly one vertex in common. In this article, results of above said indices for g-composite hypergraphs, where g ≥ 2 , are calculated. Further these results are used to find the Wiener index, degree distance index and Gutman index of sunflower hypergraphs and linear uniform hyper-paths.

Expected value of first Zagreb connection index in random cyclooctatetraene chain, random polyphenyls chain, and random chain network.

The Zagreb connection indices are the known topological descriptors of the graphs that are constructed from the connection cardinality (degree of given nodes lying at a distance 2) presented in 1972 to determine the total electron energy of the alternate hydrocarbons. For a long time, these connection indices did not receive much research attention. Ali and Trinajstic [Mol. Inform. 37, Art. No. 1800008, 2018] examined the Zagreb connection indices and found that they compared to basic Zagreb indices and that they provide a finer value for the correlation coefficient for the 13 physico-chemical characteristics of the octane isomers. This article acquires the formulae of expected values of the first Zagreb connection index of a random cyclooctatetraene chain, a random polyphenyls chain, and a random chain network with l number of octagons, hexagons, and pentagons, respectively. The article presents extreme and average values of all the above random chains concerning a set of special chains, including the meta-chain, the ortho-chain, and the para-chain.

Edge Mostar Indices of Cacti Graph With Fixed Cycles.

Topological invariants are the significant invariants that are used to study the physicochemical and thermodynamic characteristics of chemical compounds. Recently, a new bond additive invariant named the Mostar invariant has been introduced. For any connected graph ℋ , the edge Mostar invariant is described as M o e ( ℋ ) = ∑ g x ∈ E ( ℋ ) | m ℋ ( g ) - m ℋ ( x ) | , where m ℋ ( g ) ( or  m ℋ ( x ) ) is the number of edges of ℋ lying closer to vertex g (or x) than to vertex x (or g). A graph having at most one common vertex between any two cycles is called a cactus graph. In this study, we compute the greatest edge Mostar invariant for cacti graphs with a fixed number of cycles and n vertices. Moreover, we calculate the sharp upper bound of the edge Mostar invariant for cacti graphs in ℭ ( n , s ) , where s is the number of cycles.

Bounds for the general sum-connectivity index of composite graphs.

The general sum-connectivity index is a molecular descriptor defined as [Formula: see text], where [Formula: see text] denotes the degree of a vertex [Formula: see text], and α is a real number. Let X be a graph; then let [Formula: see text] be the graph obtained from X by adding a new vertex [Formula: see text] corresponding to each edge of X and joining [Formula: see text] to the end vertices of the corresponding edge [Formula: see text]. In this paper we obtain the lower and upper bounds for the general sum-connectivity index of four types of graph operations involving R-graph. Additionally, we determine the bounds for the general sum-connectivity index of line graph [Formula: see text] and rooted product of graphs.