Let G be a collection of graphs with n vertices. We present a simple description of [G]χ = {H ∈ G : χ(H) = χ(G)} where χ denotes the Randić index. We associate to G a Q-linear map ρ : Qm → Qk (for some integers k, m depending on G) such that the kernel of ρ contains the necessary information to describe [G]χ in terms of linear equations. These results provide precise tools for analyzing the beh...

Randić index is one of the most famous topological graph indices. The energy a was defined more than four decades ago for its molecular applications. classical modeling molecule as sum absolute values all eigenvalues adjacency matrix corresponding to graph. There are several other versions notion obtained using types matrices. In this paper, we introducing and investigating type Hadi RHE(G) G, ...

A topological descriptor is regarded as a numerical parameter derived by using mathematical tools from the molecular graph of different chemical structures. The theory paramount section chemistry. In this section, there are many parameters, that have very useful characteristics to study structure chemicals. article, we investigate indices concealed non-kekulean benzenoid hydrocarbon graph. We w...

Topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is a delightful playground for the exploration of proof techniques in Discrete Mathematics and its results have applications in many areas of sciences. One of the useful indic...

The Generalised Randić index R−α(T ) of a tree T is the sum over the edges uv of T of (d(u)d(v))−α where d(x) is the degree of the vertex x in T . For all α > 0, we find the minimal constant βc = βc(α) such that for all trees on at least 3 vertices R−α(T ) ≤ βc(n + 1) where n = |V (T )| is the number of vertices of T . For example, when α = 1, βc = 15 56 . This bound is sharp up to the additive...