• INDEPENDENT -SET = {[G, k] : G is an undirected graph with an independent set of vertices I ⊆ V (G) of size ≥ k} where a subset I is independent iff it contains no edges of G. – Guess a set I of size k. Verify that it contains no edges of G. • CLIQUE = {[G, k] : G is an undirected graph with an independent set of vertices C ⊆ V (G) of size ≥ k} where a subset C is a clique iff every edge on t...

Abstract Heterogeneous composites of metalloporphyrins with TiO 2 possess exceptional photosensitizing properties, which works efficiently in degradation organic pollutants. Herein, vanadium porphyrin complex {VO(TPP)} was loaded on photocatalyst {VO(TPP)–TiO } by the wet impregnation method. The as-prepared catalysts were characterized to analyze physicochemical properties and photocatalytic 4...