The super connectivity of augmented cubes

A note on "The super connectivity of augmented cubes"

Article history: Received 8 June 2008 Received in revised form 13 January 2009 Available online 14 February 2009 Communicated by A.A. Bertossi

The Super Spanning Connectivity of the Augmented Cubes

A k-container C(u, v) of G between u and v is a set of k internally disjoint paths between u and v. A k-container C(u, v) of G is a k∗-container if it contains all nodes of G. A graph G is k∗connected if there exists a k∗-container between any two distinct nodes. The spanning connectivity of G, κ∗(G), is defined to be the largest integer k such that G is w∗-connected for all 1 ≤ w ≤ k if G is a...

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

Super-connectivity and super-edge-connectivity for some interconnection networks

Let G 1⁄4 ðV ;EÞ be a k-regular graph with connectivity j and edge connectivity k. G is maximum connected if j 1⁄4 k, and G is maximum edge connected if k 1⁄4 k. Moreover, G is super-connected if it is a complete graph, or it is maximum connected and every minimum vertex cut is fxjðv; xÞ 2 Eg for some vertex v 2 V ; and G is super-edge-connected if it is maximum edge connected and every minimum...

The augmented Zagreb index, vertex connectivity and matching number of graphs

Let $Gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. Denote by $Upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. In the classes of graphs $Gamma_{n,kappa}$ and $Upsilon_{n,beta}$, the elements having maximum augmented Zagreb index are determined.