For a graph G, let σ(G) = ∑ uv∈E(G) 1 √ dG(u)+dG(v) ; this defines the sum-connectivity index σ(G). More generally, given a positive function t, the edge-weight t-index t(G) is given by t(G) = ∑ uv∈E(G) t(ω(uv)), where ω(uv) = dG(u) + dG(v). We consider extremal problems for the t-index over various families of graphs. The sum-connectivity index satisfies the conditions imposed on t in each ext...

The general sum-connectivity index of a graph $G$ is defined as $chi_{alpha}(G)= sum_{uvin E(G)} (d_u + d_{v})^{alpha}$ where $d_{u}$ is degree of the vertex $uin V(G)$, $alpha$ is a real number different from $0$ and $uv$ is the edge connecting the vertices $u,v$. In this note, the problem of characterizing the graphs having extremum $chi_{alpha}$ values from a certain collection of polyomino ...

Du, Zhou and Trinajstić [J. Math. Chem., 48, pp. 697–703, 2010] proved that in the set of n-vertex connected unicyclic graphs G with n ≥ 3, for –1 ≤ α < 0, the graph consisting of a triangle and n – 3 pendant vertices adjacent to the same vertex of this triangle is the unique graph with the minimum general sum-connectivity index. In this paper, using a graph transformation and several inequalit...

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...

L-valine is a glycogen-type amino acid regarded among the necessary mammalian acids. This an that essential for protein synthesis. N-salicylidene-L-valine gaining lot of attention because its unique structure and increased catalytic cytotoxic activity. We explore chain supramolecular dialkyltin complexes 2, 3, 4 to learn more about this features regarding topological indices. computed first sec...

Let G be a simple connected graph in chemical graph theory and uν e = be an edge of G. The Randić index ( ) G χ and sum-connectivity ( ) G X of a nontrivial connected graph G are defined as the sum of the weights ν ud d 1 and ν u d d + 1 over all edges ν u e = of G, respectively. In this paper, we compute Randić ( ) G χ and sum-connectivity ( ) G X indices of V-phenylenic nanotubes and nanotori.

The Harary index of a graph is defined as the sum of reciprocals of distances between all pairs of vertices of the graph. In this paperweprovide anupper boundof theHarary index in terms of the vertex or edge connectivity of a graph. We characterize the unique graph with themaximumHarary index among all graphs with a given number of cut vertices or vertex connectivity or edge connectivity. In ad...