The Wiener index of a graph is defined as the sum of distances between all pairs of vertices in a connected graph. Wiener index correlates well with many physio chemical properties of organic compounds and as such has been well studied over the last quarter of a century. In this paper we prove some general results on Wiener Index for graphs using degree sequence.

The generalized Mycielskians are the generalization of the Mycielski graphs, which were introduced by Mycielski in 1955. A topological index is a numeric parameter mathematically derived from a graph and is invariant under automorphism of graphs. Topological indices are widely used for establishing correlations between the structure of a molecular compound and its different physico-chemical pro...

In this paper we investigate focusing properties of graded index (GRIN) photonic crystal (PC) structures which are composed of different materials with different refractive indices. GRIN PC structure is constructed from air holes in dielectric background. The holes radii are varied in the normal direction to the propagation in such a way that a parabolic effective refractive index is produced. ...

upgrading recycled fiber properties has been a constant concern in pulp and paper industry. in this respect many researches has been applied. the present paper has been considered the effect of amylase enzyme in pulping stage of old corrugated container (occ). also, pre-soaking of occ (first step of pre-soaking for 6 hours in 3% consistency in different ph(s) and second step of pre-soaking at 6...

Using the replica method, we develop an analytical approach to compute the characteristic function for the probability P(N)(K,λ) that a large N×N adjacency matrix of sparse random graphs has K eigenvalues below a threshold λ. The method allows to determine, in principle, all moments of P(N)(K,λ), from which the typical sample-to-sample fluctuations can be fully characterized. For random graph m...