on the reliability wiener number

On the reliability wiener number

One of the generalizations of the Wiener number to weighted graphs is to assign probabilities to edges, meaning that in nonstatic conditions the edge is present only with some probability. The Reliability Wiener number is defined as the sum of reliabilities among pairs of vertices, where the reliability of a pair is the reliability of the most reliable path. Closed expressions are derived for t...

The reliability Wiener number of cartesian product graphs

Reliability Wiener number is a modification of the original Wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. Various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain condition...

the reliability wiener number of cartesian product graphs

reliability wiener number is a modification of the original wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain condition...

On reciprocal complementary Wiener number

Wiener-Number-Related Sequences

Recently various generalizations or extensions of the now “classical” Wiener number1 have become of interest, both as regards new individual numbers2-7 and as regards sequences of numbers.8-12 Of particular interest here are those numbers of Tratch et al.2 and of Randić,3 their manner of interrelation, their formulas for trees as extended to general cycle-containing graphs, and their extension ...

The Wiener Number of the Hexagonal Net

The Wiener number of a molecular graph, or more generally of a connected graph, is equal to the sum of distances between all pairs of its vertices. A graph formed by a hexagon in the centre, surrounded by n rings of hexagonal cells, is called an n-hexagonal net. It is shown that the Wiener number of an n-hexagonal net equals i( 164n5 30n3 + n).