The m-order connectivity index mχ(G) of a molecular graph G is the sum of the weights (di1di2 · · · dim+1) 1 2 , where di1di2 · · · dim+1 runs over all paths of length m in G and di denotes the degree of vertex vi. Dendrimer is a polimer molecule with a distinctive structure that resembles the crown of a tree. In this paper we compute second-order and third-order connectivity indices of an infi...

We show that the necessary divisibility conditions for the existence of a σ-resolvable BIBD(v, k, λ) are sufficient for large v. The key idea is to form an auxiliary graph based on an [r, k]-configuration with r = σ, and then edge-decompose the complete λ-fold graph K (λ) v into this graph. As a consequence, we initiate a similar existence theory for incomplete designs with index λ. ∗ Supported...

A typical B-rep describes a solid in its full detail. Operations that locally analyze the B-rep usually process the entire B-rep due to the lack of spatial ordering of its topological entities. For very complex objects, this global processing is time consuming and yet unnecessary. One approach in avoiding the global processing is to use several B-reps of different levels of detail. However, thi...

Abstract Packing topological entropy is a dynamical analogy of the packing dimension, which can be viewed as counterpart Bowen entropy. In present paper we give systematic study for continuous G -action system $(X,G)$ , where X compact metric space and countable infinite discrete amenable group. We first prove variational principle entropy: any Borel subset Z equals supremum upper local over al...