论文标题
2边彩色图的色多项式
Chromatic polynomials of 2-edge coloured graphs
论文作者
论文摘要
使用$ 2 $边缘色的颜色的定义，这些图形衍生自$ 2 $ edge颜色的图形同态，我们将色度多项式的定义扩展到$ 2 $ - edge-gedge-through。我们发现该多项式的前三个系数的封闭形式概括了图形多项式的已知结果。当每个顶点都在两种颜色的边缘时，我们对具有色度多项式等于色度多项式的色度多项式的$ 2 $ edge颜色的图进行了分类。最后，我们研究了该多项式的根部的行为，突出了图形多项式中未见的行为。
Using the definition of colouring of $2$-edge-coloured graphs derived from $2$-edge-coloured graph homomorphism, we extend the definition of chromatic polynomial to $2$-edge-coloured graphs. We find closed forms for the first three coefficients of this polynomial that generalize the known results for the chromatic polynomial of a graph. We classify those $2$-edge-coloured graphs that have a chromatic polynomial equal to the chromatic polynomial of the underlying graph, when every vertex is incident to edges of both colours. Finally, we examine the behaviour of the roots of this polynomial, highlighting behaviours not seen in chromatic polynomials of graphs.
