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The concept of rainbow connection was introduced by . It is fairly interesting and recently quite a lot papers have been published about it. In this survey we attempt to bring together most of the results and papers that dealt with it. We begin with an introduction, and then try to organize the work into five categories, including (strong) rainbow connection number, rainbow k-connectivity, k-rainbow index, rainbow vertex-connection number, algorithms and computational complexity. This survey also contains some conjectures, open problems or questions.

A complex adjacency matrix of a mixed graph is introduced in the present paper, which is a Hermitian matrix and called the Hermitian-adjacency matrix. It incorporates both adjacency matrix of an undirected graph and skew-adjacency matrix of an oriented graph. Some of its properties are studied. Furthermore, properties of its characteristic polynomial are studied. Cospectral problems among mixed graphs, including mixed graphs and their underlying graphs, oriented graphs and their underlying graphs, are studied. We give equivalent conditions for a mixed graph (especially oriented graph) that share the same spectrum with its underlying graph. As a consequence, we reconfirm a conjecture which was proposed by Cui and Hou in Ref. [8]. We also show that the spectrum of the Hermitian matrix of a mixed graph is invariant when changing the value of any its cut edge (if any). Correspondingly, an energy of a mixed graph is introduced and called the Hermitian energy. It incorporates both the energy of an undirected graph and the skew energy of an oriented graph. Some of its bounds are given. Especially, the mixed graphs with optimal upper bound of Hermitian energy are characterized. An infinite family of mixed graphs attaining the maximum Hermitian energy is constructed. Moreover, the Hermitian energy of a mixed tree is showed to be equal to ✩ 183 the energy of its underlying tree. Finally, the integral formula for Hermitian energy of a mixed graph is given.

High-throughput synthesis of well-defined polymer nano-objects has long been an attractive yet challenging topic in the area of polymer chemistry and material science. Herein, we report an enzyme-assisted photoinitiated polymerizationinduced self-assembly (photo-PISA) approach to prepare well-defined AB diblock or ABC triblock copolymer nano-objects at room temperature in open vessels and multiwell plates. Kinetic studies indicated that the presence of glucose oxidase (GOx) endowed the polymerizations with excellent oxygen tolerance. Good control was maintained during the enzyme-assisted photo-PISA process. This method facilitates high-throughput PISA, allowing for the construction of a detailed phase diagram in a rather short time. We also demonstrate the potential bio-related application of this method by the successful encapsulation of horseradish peroxidase (HRP) and bovine serum albumin (BSA) into self-assembled polymer vesicles without compromising protein activities. This robust oxygen-tolerant PISA approach leads to unprecedented access to well-defined polymer nanoobjects for nonexperts.

Boron–nitrogen coordination in polyurethane elastomers enhances the dynamics of the boronic ester while introduces inter- and intra-molecular interactions, leading to mechanical robustness and excellent self-healing efficiency simultaneously.