based on the randic suggestion of the resolution of a structure into shape, size, and function an index representing structure-catabolic fate relationships of amino acids is constructed. the index obtained by multiplying three factors; (nb2 + nr), nc and m; representing shape, size and function respectively, where nb2 = number of double bonds, nr = number of rings, nc = number of carbon atoms, ...

A lot of research and various techniques have been devoted for finding the topological descriptor Wiener index, but most of them deal with only particular cases. There exist three regular plane tessellations, composed of the same kind of regular polygons namely triangular, square, and hexagonal. Using edge congestion-sum problem, we devise a method to compute the Wiener index and demonstrate th...

let $d$ be a digraph with vertex set $v(d)$. for vertex $vin v(d)$, the degree of $v$,denoted by $d(v)$, is defined as the minimum value if its out-degree and its in-degree.now let $d$ be a digraph with minimum degree $deltage 1$ and edge-connectivity$lambda$. if $alpha$ is real number, then the zeroth-order general randic index is definedby $sum_{xin v(d)}(d(x))^{alpha}$. a digraph is maximall...

this note introduces a new general conjecture correlating the dimensionality dt of an infinitelattice with n nodes to the asymptotic value of its wiener index w(n). in the limit of large nthe general asymptotic behavior w(n)≈ns is proposed, where the exponent s and dt are relatedby the conjectured formula s=2+1/dt allowing a new definition of dimensionality dw=(s-2)-1.being related to the topol...

fullerenes are closed−cage carbon molecules formed by 12 pentagonal and n/2 – 10hexagonal faces, where n is the number of carbon atoms. patrick fowler in his lecture inmcc 2009 asked about the wiener index of fullerenes in general. in this paper werespond partially to this question for an infinite class of fullerenes with exactly 10ncarbon atoms. our method is general and can be applied to full...

All the drugs used as analgesic agent have some systemic side effects. For the researchers, the prospects of overcoming the side effects of a drug, achieving an effect at a much lower dose is very attractive. Modification of the structure of a known drug is one way to develop new drugs. For this purpose, we have optimized the pyrimidobenzimidazole derivatives using molecular modeling studies. Q...

Abstract. In this paper Reverse Wiener index, Reverse Detour Wiener index, Reverse Circular Wiener index Reverse Harary index, Reverse Detour Harary index, Reverse Circular Harary index, Reverse Reciprocal Wiener index, Reverse Detour Reciprocal Wiener index, Reverse Circular Reciprocal Wiener index, Reverse Hyper Wiener index, Reverse, Detour Hyper Wiener index, Reverse Circular Hyper Wiener i...

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...