Locally exchanged twisted cubes: Connectivity and super connectivity

• A new interconnection network called locally exchanged twisted cube (LETQ), is proposed.
• We obtain some basic properties of LETQ including isomorphism, decomposition and Hamiltonicity.
• We determine the connectivity and the super connectivity of LETQ.

Connectivity κ(G)κ(G) (resp., super connectivity κ′(G)κ′(G)) of a graph G   is the minimum number of vertices whose removal leaves the remaining graph disconnected or trivial (resp., the remaining graph disconnected and without isolated vertex). These two parameters are important for interconnection networks and can be used to measure reliability in such networks. In this paper, a new interconnection network called locally exchanged twisted cube (LETQ for short), denoted LeTQ(s,t)LeTQ(s,t), is proposed. We obtain some basic properties of LETQ including isomorphism, decomposition, Hamiltonicity and connectivity. In particular, we determine κ(LeTQ(s,t))=min⁡{s+1,t+1}κ(LeTQ(s,t))=min⁡{s+1,t+1} and κ′(LeTQ(s,t))=min⁡{2s,2t}κ′(LeTQ(s,t))=min⁡{2s,2t} for s,t⩾1s,t⩾1.