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

<abstract><p>Let $ G be a simple connected graph with the vertex set V(G) and d_{B}(u, v) biharmonic distance between two vertices u v in $. The index BH(G) of is defined as</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ = \frac{1}{2}\sum\limits_{u\in V(G)}\sum\limits_{v\in V(G)}d_{B}^2(u, n\sum\limits_{i 2}^{n}\frac{1}{\lambda_i^2...

Recently, a novel degree-based molecular structure descriptor, called Sombor index was introduced. Let G=(V(G),E(G)) be graph. Then, the of G is defined as SO(G)=?uv?E(G)dG2(u)+dG2(v). In this paper, we give some lemmas that can used to compare indices between two graphs. With these lemmas, determine graph with maximum SO among all cacti n vertices and k cut edges. Furthermore, unique p pendant...

Let <em>G</em> be a subgroup of <em>S</em><sub>n</sub>. For <em>x ∈ G</em>, the index <em>x</em> in is denoted by <em>ind x</em> minimal number 2-cycles needed to express as product. In this paper, we define new kind graph on <em>G</em>, namely and <em>Γ</em><sup>ind</sup><em>(G)&lt...

‎the narumi-katayama index was the first topological index defined‎ ‎by the product of some graph theoretical quantities‎. ‎let $g$ be a ‎simple graph with vertex set $v = {v_1,ldots‎, ‎v_n }$ and $d(v)$ be‎ ‎the degree of vertex $v$ in the graph $g$‎. ‎the narumi-katayama ‎index is defined as $nk(g) = prod_{vin v}d(v)$‎. ‎in this paper,‎ ‎the narumi-katayama index is generalized using a $n$-ve...