18 Results Found

In this work, we determine the maximum general Randić index (a general symmetric function of vertex degrees) for ${\eta }_0\le \eta <0$ among all n-vertex unicyclic graphs with a fixed maximum degree $\mathsf{\Delta }$ and the maximum and the second maximum general Randić index f...

For a graph G without isolated vertices, the inverse degree of a graph G is defined as $ID(G)={\sum }_{u\in V(G)}d{(u)}^{-1}$ where $d(u)$ is the number of vertices adjacent to the vertex u in G. By replacin...

In this work, we obtained new results relating the generalized atom-bond connectivity index with the general Randić index. Some of these inequalities for $AB{C}_{\alpha }$ improved, when $\alpha =1/2$, known results on the $ABC$ index. Moreover, in order to obtain our resu...

A Topological index also known as connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology a...

Let G be a simple undirected graph on n vertices. V. Nikiforov studied hybrids of $A_G$ and $D_G$ and defined the matrix $A_{\alpha }^G$ for every real $\alpha \in [0,1]$ as $A_{\alpha }^G=\alpha D_G+(1-\alpha )A_G.$ In this paper, we define the generalized Randi&...

The utilizations of graph theory in chemistry and in the study of molecule structures are more than someone’s expectations, and, lately, it has increased exponentially. In molecular graphs, atoms are denoted by vertices and bonds by edges. In t...

In 1997, Sierpinski graphs, $S(n,k)$, were obtained by Klavzar and Milutinovic. The graph $S(1,k)$ represents the complete graph $K_k$ and $S(n,3)$ is known as the graph of the Tower of Hanoi. Through generalizing the notion of a Sierpinski graph, a graph nam...

This paper is mainly concerned with the study of two bond incident degree (BID) indices, namely the variable sum exdeg index $SE{I}_a$ and the general zeroth-order Randić index ${}^{0}R_{\alpha }$. The minimum values of $SE{I}_a$ and ${}^{0}R_{\alpha }$ in the class of all t...

In chemical graph theory, a topological index is a numerical representation of a chemical network, while a topological descriptor correlates certain physicochemical characteristics of underlying chemical compounds besides its chemical representation....

A topological index is a numerical representation of a chemical structure, while a topological descriptor correlates certain physico-chemical characteristics of underlying chemical compounds besides its numerical representation. A large number of pro...

Titania is one of the most comprehensively studied nanostructures due to their widespread applications in the production of catalytic, gas sensing, and corrosion-resistant materials. M-polynomial of nanotubes has been vastly investigated, as it produ...

Chemical graph theory plays an important role in modeling and designing any chemical structure. The molecular topological descriptors are the numerical invariants of a molecular graph and are very useful for predicting their bioactivity. In this pape...

Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices ar...

The l-generalized quasi tree is a graph G for which we can find $W\subset V\left(G\right)$ with $\left|W\right|=l$ such that $G-W$ is a tree but for an arbitrary $Y\subset V\left(G\right)$ with $\left|Y\right|<l$, $G-Y$ is not a tree. In this paper, inequalities with respect to zeroth-order Randi...

The bismuth tri-iodide $(Bi{I}_3)$ is an inorganic compound. It is the result of the response of bismuth and iodine, which has inspired enthusiasm for subjective inorganic investigation. The topological indices are the numerical invariants of...

The vertex k-partiteness of graph G is defined as the fewest number of vertices whose deletion from G yields a k-partite graph. In this paper, we characterize the extremal value of the reformulated first Zagreb index, the multiplicative-sum Zagreb in...

A topological index is a number generated from a molecular structure (i.e., a graph) that indicates the essential structural properties of the proposed molecule. Indeed, it is an algebraic quantity connected with the chemical structure that correlate...

In the studies of quantitative structure–activity relationships (QSARs) and quantitative structure–property relationships (QSPRs), graph invariants are used to estimate the biological activities and properties of chemical compounds. In th...