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For a triangulated category with a bounded t-structure, we prove that there is a bijection between wide subcategories of its heart and thick subcategories of the triangulated category which are closed under the corresponding cohomological functor. We prove that a finite-dimensional triangular algebra over an algebraically closed field is hereditary if and only if any thick subcategory of the bounded derived category is closed under the usual cohomological functor.

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Let G be a graph and σ:E(G)→{+1,−1} be a mapping. The pair (G,σ), denoted by Gσ, is called a signed graph. A (proper) l-edge coloring γ of Gσ is a mapping from each vertex–edge incidence of Gσ to Mq such that γ(v,e)=−σ(e)γ(w,e) for each edge e=vw, and no two vertex–edge incidences have the same color; that is, γ(v,e)≠γ(v,f). The chromatic index is the minimal number q such that Gσ has a proper q-edge coloring, denoted by χ′(Gσ). In 2020, Behr proved that the chromatic index of a signed graph is its maximum degree or maximum plus one. In this paper, we considered the chromatic index of the signed generalized Petersen graph GP(n,2) and show that its chromatic index is its maximum degree for most cases. In detail, we proved that (1) χ′(GPσ(n,2))=3 if n≡3 mod 6(n≥9); (2) χ′(GPσ(n,2))=3 if n=2p(p≥4).

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