The realization of the potential of carbon nanotori as elements of nanoscale devices based on their recently predicted unusual properties requires a thorough understanding of contacting these nanostructures. We carried out a series of calculations of the electric conductance of carbon nanotori contacted by single-wall carbon nanotubes to shed light on the effects of the geometry as well as the ...

The PI polynomial of a molecular graph is defined to be the sum X(|E(G)|-N(e)) + |V(G)|(|V(G)|+1)/2 - |E(G)| over all edges of G, where N(e) is the number of edges parallel to e. In this paper, the PI polynomial of the phenylenic nanotubes and nanotori are computed. Several open questions are also included.

Let G be a graph. The distance d(u,v) between the vertices u and v of the graph G is equal to the length of a shortest path that connects u and v. The Wiener index W(G) is the sum of all distances between vertices of G, whereas the hyper-Wiener index WW(G) is defined as WW(G)=12W(G)+12@?"{"u","v"}"@?"V"("G")d (u,v)^2. In this paper the hyper-Wiener indices of the Cartesian product, composition,...

The 1-, 2-, and 3-dimensional structures obtained from conjugated rings of carbon atoms are reviewed. They include finite small and large molecules (benzenoids, collarenes, beltenes, cyclacenes, cyclophenacenes, Möbius analogs, nanotori) and infinite macromolecules, nets and tilings (graphene, defected graphene, fractal benzenoids, nano-tubes, nano-cones, etc.). A few challenges for future expe...

Persistent currents in rings constructed from carbon nanotubes are investigated theoretically. After studying the contribution of finite temperature or quenched disorder on covalent rings, the complexity due to the bundle packing is addressed. The case of interacting nanotori and self-interacting coiled nanotubes are analyzed in details in relation with experiments.

Let G be a simple connected graph in chemical graph theory and uν e = be an edge of G. The Randić index ( ) G χ and sum-connectivity ( ) G X of a nontrivial connected graph G are defined as the sum of the weights ν ud d 1 and ν u d d + 1 over all edges ν u e = of G, respectively. In this paper, we compute Randić ( ) G χ and sum-connectivity ( ) G X indices of V-phenylenic nanotubes and nanotori.