The distribution, characteristics of extracellular polymeric substances (EPS) of Phanerochaete chrysosporium under Pb2+ stress and the influence on Pb removal were investigated. Polysaccharides was found to be the main composition in both soluble EPS (SEPS) and bounded EPS (BEPS). More polysaccharides and protein in BEPS were detected with the increased Pb2+ concentration. The ratio of Pb amount distributed in BEPS to the total Pb removed by the fungal biomass gradually decreased from 91.66 to 61.27% in group with 50 mg/L of initial Pb2+, but kept at about 35% or 25% in groups with higher Pb2+. It implies that BEPS played a certain role in the lead removal process, and the role of BEPS was relatively more important in the removal of lower concentration of Pb2+ and in the initial period of Pb removal. With FTIR analysis and Pb2+ adsorption experiment, more effective functional groups and better Pb2+ adsorption capacity was demonstrated in BEPS than in SEPS. SEM–EDS analysis demonstrated that part of Pb immobilized in BEPS was in the form of Pb precipitation. The increased molecular weight in SEPS and more polysaccharides in BEPS were probably beneficial for the adhesion of Pb precipitation.

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a b s t r a c tA fullerene graph F is a planar cubic graph with exactly 12 pentagonal faces and other hexagonal faces. A set H of disjoint hexagonsform a resonant pattern. It was known that each fullerene graph is 1-resonant and there are only nine fullerene graphs that are 3-resonant. In this paper, we show that the fullerene graphs which do not contain the subgraph L or R as illustrated in Fig. 1 are 2-resonant except for the specific eleven graphs. This result implies that each IPR fullerene is 2-resonant.

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A graph $G$ is said to be distance-balanced if for any edge $uv$ of $G$, the number of vertices closer to $u$ than to $v$ is equal to the number of vertices closer to $v$ than to $u$. Let $GP(n,k)$ be a generalized Petersen graph. Jerebic, Klavžar, and Rall [Distance-balanced graphs, Ann. Comb. 12 (2008) 71–79] conjectured that: For any integer $k\geq 2$, there exists a positive integer $n_0$ such that the $GP(n,k)$ is not distance-balanced for every integer $n\geq n_0$. In this note, we give a proof of this conjecture.