The chemical potential for a novel intrinsic graph metric, the resistance distance, is briefly recalled, and then a number of »sum rules« for this metric are established. »Global« and »local« types of sum rules are identified. The sums in the »global« sum rules are graph invariants, and the sum rules provide inter-relations amongst different invariants, some involving the resistance distance wh...

Relationship between the topochemical indices and 5-HT6 binding affinity of 3-ethyl-1H-indoles has been investigated. Wiener’s topochemical index a distance-based topochemical descriptor, eccentric connectivity topochemical index and augmented eccentric connectivity topochemical index both adjacency-cum-distance based topochemical descriptors were used for the present investigation. A dataset c...

The eccentricity e(u) of a vertex u in a digraph G is the maximum distance from u to any other vertex in G. A vertex v is an eccentric vertex of u if the distance from u to v is equal to e(u). The eccentric digraph ED(G) of a digraph G has the same vertex set as G, but with an arc from u to v in ED(G) if and only if v is an eccentric vertex of u in G. Given a positive integer k, the k iterated ...

Eccentric coloring is a new variation of coloring, where higher numbered colors can not be used as freely as lower numbered colors. In addition there is a correspondence between the eccentricity (max distance) of a vertex and the highest legal color for that vertex. In this note we investigate eccentric coloring of trees. We give the eccentric chromatic number or a bound on the eccentric chroma...

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 exact formula for the Wiener index. As application we calculate the Schultz index and modified Schultz index of this...

The eccentric sequence of a connected graph \(G\) is the nondecreasing eccentricities its vertices. Wiener index sum distances between all unordered pairs vertices \(G\). unique trees that minimise among with given were recently determined by present authors. In this paper we show these results hold not only for index, but large class distance-based topological indices which term Wiener-type in...