Induced subgraphs with maximum number of edges on crossed cubes

In several parallel distributed processing systems, processors are connected on the basis of interconnection networks. The topological structure of an interconnection network can be modeled as a loopless undirected graph G = (V,E) where V is the vertex set and E the edge set of G. For a vertex subset V' ̃ V of graph G, the subgraph of G induced by V', denoted by G[V'], is a graph with vertex set V' and all the edges of G with both ends of vertices in V'. An m-induced subgraph of a graph is such one which induced by m vertices. A maximum m-induced subgraph of a graph G, denoted by V
^max
m
(G), can be defined as V
^max
m
(G) = {G[V'] | max
V'̃V,|V|=m |E(G[V'])|
. The results of maximum m-induced subgraph can be applied to the measurement of fault tolerance and bandwidth of networks, and also relate to electromechanical or optical sensors. Abdel-Ghaffar has shown the maximum m-induced subgraphs on the n-dimensional hypercubes in 2003. In this paper, we investigate in constructing the maximum m-induced subgraphs and working out the number of edges of the maximum m-induced subgraphs on the n-dimensional crossed cubes.