Abstract We prove a moment identity on the Wiener space that extends the Skorohod isometry to arbitrary powers of the Skorohod integral on the Wiener space. As simple consequences of this identity we obtain sufficient conditions for the Gaussianity of the law of the Skorohod integral and a recurrence relation for the moments of second order Wiener integrals. We also recover and extend the suffi...

The Wiener index of a graph is the sum of the distances between all pairs of vertices, it has been one of the main descriptors that correlate a chemical compound’s molecular graph with experimentally gathered data regarding the compound’s characteristics. In [1], the tree that minimizes the Wiener index among trees of given maximal degree is studied. We characterize trees that achieve the maxim...

Polynomial interpolation can be used to obtain closed formulas for topological indices of infinite series of molecular graphs. The method is discussed and its advantages and limitations are pointed out. This is illustrated on fullerenes C12k+4 and four topological indices: the Wiener index, the edge Wiener index, the eccentric connectivity index, and the reverse Wiener index. The results for th...

The Wiener index of a graph Gis defined as W(G) =1/2[Sum(d(i,j)] over all pair of elements of V(G), where V (G) is the set of vertices of G and d(i, j) is the distance between vertices i and j. In this paper, we give an algorithm by GAP program that can be compute the Wiener index for any graph also we compute the Wiener index of HAC5C7[p, q] and HAC5C6C7[p, q] nanotubes by this program.

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For a connected graph G and an non-empty set S ⊆ V (G), the Steiner distance dG(S) among the vertices of S is defined as the minimum size among all connected subgraphs whose vertex sets contain S. This concept represents a natural generalization of the concept of classical graph distance. Recently, the Steiner Wiener index of a graph was introduced by replacing the classical graph distance used...

The Wiener Index, or the Wiener Number, also known as the “sum of distances” of a connected graph, is one of the quantities associated with a molecular graph that correlates nicely to physical and chemical properties, and has been studied in depth. An index proposed by Schultz is shown to be related to the Wiener Index for trees, and Ivan Gutman proposed a modification of the Schultz index with...