Connectivity! Connectivity! Connectivity! May You Be More Connected Than Ever!!

Eccentric Connectivity and Augmented Eccentric Connectivity Indices of N-Branched Phenylacetylenes Nanostar Dendrimers

eccentric connectivity and augmented eccentric connectivity indices of n-branched phenylacetylenes nanostar dendrimers

High connectivity keeping connected subgraph

It was proved by Mader that, for every integer l, every k-connected graph of sufficiently large order contains a vertex set X of order precisely l such that G−X is (k − 2)-connected. This is no longer true if we require X to be connected, even for l = 3. Motivated by this fact, we are trying to find an ”obstruction” for k-connected graphs without such a connected subgraph. It turns out that the...

On $(α, β)$−Linear Connectivity

In this paper we introduce $(alpha,beta)-$linear connected spaces for nonzero cardinal numbers $alpha$ and $beta$. We show that $(alpha,beta)-$linear connectivity approach is a tool to classify the class of all linear connected spaces.

Eccentric Connectivity Index: Extremal Graphs and Values

Eccentric connectivity index has been found to have a low degeneracy and hence a significant potential of predicting biological activity of certain classes of chemical compounds. We present here explicit formulas for eccentric connectivity index of various families of graphs. We also show that the eccentric connectivity index grows at most polynomially with the number of vertices and determine ...