The Wiener index of a graph G is defined as W(G) = 1/2∑{x,y}⊆V(G)d(x,y), where V(G) is the set of all vertices of G and for x,y ∈ V(G), d(x,y) denotes the length of a minimal path between x and y. In this paper, we first report our recent results on computing Wiener, PI and Balaban indices of some nanotubes and nanotori. Next, the PI and Szeged indices of a new type of nanostar dendrimers are c...

Finite simple graphs are a playground for classical areas of mathematics. We illustrate this by looking at some results.

In running mass inflation and hybrid inflation models it is possible that the inflaton field will fragment into non-topological solitons, resulting in a highly inhomogeneous post-inflation era prior to reheating. In supersymmetric models with a conventional homogeneous post-inflation era, the dynamics of flat direction scalars are determined by cH corrections to the mass squared terms (where |c...

A Heffter array is an m× n matrix with nonzero entries from Z2mn+1 such that i) every row and column sum to 0, and ii) exactly one of each pair {x,−x} of nonzero elements appears in the array. We construct some Heffter arrays. These arrays are used to build current graphs used in topological graph theory. In turn, the current graphs are used to embed the complete graph K2mn+1 so that the faces ...

We examine the relation between topological entropy, invertability, and prediction in topological dynamics. We show that topological determinism in the sense of Kamińsky Siemaszko and Szymański imposes no restriction on invariant measures except zero entropy. Also, we develop a new method for relating topological determinism and zero entropy, and apply it to obtain a multidimensional analog of ...

A VDB topological index is defined as

The gapless surface states of topological insulators (TI) can potentially be used to detect and harvest low-frequency infrared light. Nonetheless, it was shown that significant surface photocurrents due to light with frequency below the bulk gap are rather hard to produce. Here we demonstrate that a periodic magnetic pattern added to the surface dramatically enhances surface photocurrents in TI...