The Super Spanning Connectivity of the Augmented Cubes

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.

The super connectivity of augmented cubes

The augmented cube AQn, proposed by Choudum and Sunitha [S.A. Choudum, V. Sunitha, Augmented cubes, Networks 40 (2) (2002) 71–84], is a (2n− 1)-regular (2n− 1)-connected graph (n = 3). This paper determines that the super connectivity of AQn is 4n− 8 for n 6 and the super edge-connectivity is 4n− 4 for n 5. That is, for n 6 (respectively, n 5), at least 4n− 8 vertices (respectively, 4n− 4 edges...

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

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...