Given a 3-colorable graph $X$, the 3-coloring complex $B\left(X\right)$ is the graph whose vertices are all the independent sets which occur as color classes in some 3-coloring of $X$. Two color classes $C,D\in V\left(B\left(X\right)\right)$ are joined by an edge if $C$ and $D$ appear together in a 3-coloring of $X$. The graph $B\left(X\right)$ is 3-colorable. Graphs for which $B\left(B\left(X\right)\right)$ is isomorphic to $X$ are termed reflexive graphs. In this paper, we consider 3-edge-colorings of cubic graphs for which we allow half-edges. Then we consider the 3-coloring complexes of their line graphs. The main result of this paper is a surprising outcome that the line graph of any connected cubic triangle-free outerplanar graph is reflexive. We also exhibit some other interesting classes of reflexive line graphs.

给定一个三色图 $X$，三色复合物 $乙（X）$ 是图形，其顶点是所有独立的集合，在颜色的某些3色中作为颜色类出现 $X$。两种颜色等级$C，d\in V（乙（X））$ 如果被边缘连接 $C$ 和 $d$ 一起以3种颜色出现 $X$。图$乙（X）$是3色的。的图形$乙（乙（X））$ 同构 $X$被称为自反图。在本文中，我们考虑三次图的3边着色，允许我们使用半边。然后我们考虑其线图的3色复合体。本文的主要结果是令人惊讶的结果，即任何连接的立方无三角形外平面图的线图都是自反的。我们还展示了自反折线图的其他一些有趣的类别。