Extending Connectivity Functions on R

Extending Functions in the Model Subspaces of H^2(R) to C

Extending connectivity functions on R n ✩

A function f :Rn →R is a connectivity function if for every connected subset C of Rn the graph of the restriction f C is a connected subset of Rn+1, and f is an extendable connectivity function if f can be extended to a connectivity function g :Rn+1 → R with Rn embedded into Rn+1 as Rn × {0}. There exists a connectivity function f :R→ R that is not extendable. We prove that for n 2 every connec...

On General Sum-Connectivity Index of Benzenoid Systems and Phenylenes

A Note on Atom Bond Connectivity Index

The atom bond connectivity index of a graph is a new topological index was defined by E. Estrada as ABC(G)  uvE (dG(u) dG(v) 2) / dG(u)dG(v) , where G d ( u ) denotes degree of vertex u. In this paper we present some bounds of this new topological index.

On Second Atom-Bond Connectivity Index

The atom-bond connectivity index of graph is a topological index proposed by Estrada et al. as ABC (G)  uvE (G ) (du dv  2) / dudv , where the summation goes over all edges of G, du and dv are the degrees of the terminal vertices u and v of edge uv. In the present paper, some upper bounds for the second type of atom-bond connectivity index are computed.