Maximum Induced Subgraph of an Augmented Cube

Let ) (m max G ξ denote the maximum number of edges in a subgraph of graph G induced by m nodes. The n -dimensional augmented cube, denoted as n AQ , a variation of the hypercube, possesses some properties superior to those of the hypercube. We study the cases when G is the augmented cube n AQ . In this paper, we show that i p i r i n AQ i p m max )2 2 1 2 ( = ) ( 0 = − + ∑ ξ , where r p p p > > > 1 0 are nonnegative integers defined by i p r i m 2 = 0 = ∑ and 2 ≥ m . We then apply this formula to find the bisection width of n AQ . Keywords—Interconnection network, Augmented cube, Induced subgraph, Bisection width.