Exponential independence

Similarly as for exponential domination, the non-local nature of exponential independence leads to many interesting effects and challenges. Our results comprise exact values for special graphs as well as tight bounds and the corresponding extremal graphs. Furthermore, we characterize all graphs G for which αe(H) equals the independence number α(H) for every induced subgraph H of G, and we give an explicit characterization of all trees T with αe(T)=α(T).