In this paper, we extend the recently introduced vertex-degree-based topological index, Sombor and call it general index. The index generalizes both forgotten We present bounds in terms of other important graph parameters for also explore Nordhaus–Gaddum-type result further relations between generalized indices: Randić sum-connectivity

We consider $2$-colourings $f : E(G) \rightarrow \{ -1 ,1 \}$ of the edges a graph $G$ with colours $-1$ and $1$ in $\mathbb{Z}$. A subgraph $H$ is said to be zero-sum under $f$ if $f(H) := \sum_{e\in E(H)} f(e) =0$. study following type questions, several cases obtaining best possible results: Under which conditions on $|f(G)|$ can we guarantee existence spanning tree $G$? The types are comple...

let $gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. denote by $upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. in the classes of graphs $gamma_{n,kappa}$ and $upsilon_{n,beta}$, the elements having maximum augmented zagreb index are determined.

In theoretical chemistry, -modified Wiener index is a graph invariant topological index to analyze the chemical properties of molecular structure. In this note, we determine the minimum -modified Wiener index of graph with fixed connectivity or edge-connectivity. Our results also present the sufficient and necessary condition for reaching the lower bound.

In this paper, we introduce the atom bond connectivity E-Banhatti index and sum of a graph. Also compute these newly defined indices for wheel graphs, friendship chain silicate networks, honeycomb networks nanotubes.

The graphs having the maximum value of certain bond incident degree indices (including second Zagreb index, general sum-connectivity and zeroth-order Randi? index) in class all connected with fixed order number pendent vertices are characterized this paper. problem finding minimum values index from aforementioned is also addressed. One obtained results about first has already been proved papers...

Let G be a simple connected graph of order n. The connectivity index Rα(G) of a graph G is the sum of the weights (d(u)d(v)) of all edges uv of G, where α is a real number (α 6= 0), and d(u) denotes the degree of the vertex u. In this paper, we present some new bounds for the connectivity index of a graph G in terms of the eigenvalues of the Laplacian matrix or adjacency matrix of the graph G, ...

let g be a connected simple (molecular) graph. the distance d(u, v) between two vertices u and v of g is equal to the length of a shortest path that connects u and v. in this paper we compute some distance based topological indices of h-phenylenic nanotorus. at first we obtain an exactformula for the wiener index. as application we calculate the schultz index and modified schultz index of this ...

A real-number to molecular structure mapping is a topological index. It graph invariant method for describing physico-chemical properties of structures specific substances. In that article, We examined pentacene’s chemical composition. The research on the subsequent indices reflected in our paper, we conducted an analysis several including general randic connectivity index, first zagreb sum-con...