论文标题
集团多项式和和弦图
Clique Polynomials and Chordal Graphs
论文作者
论文摘要
$ g $的完整子图的数量的普通生成函数称为$ g $的集团多项式，并用$ c（g，x）$表示。 $ c（g，x）$的真实根称为图$ g $的集团根。 Hajiabolhasan和Mehrabadi表明，该集团多项式在间隔$ [-1,0）$中始终是真正的根源。此外，他们表明，无三角形图的类别仅具有集体根。在这里，我们通过证明$ k_4 $ free condal图的类别也只有集体根来概括他们的结果。此外，我们表明该课程始终具有一个集团的root $ -1 $。我们终于以几个重要的问题和猜想结束了本文。
The ordinary generating function of the number of complete subgraphs of $G$ is called a clique polynomial of $G$ and is denoted by $C(G,x)$. A real root of $C(G,x)$ is called a clique root of the graph $G$. Hajiabolhasan and Mehrabadi showed that the clique polynomial has always a real root in the interval $[-1,0)$. Moreover, they showed that the class of triangle-free graphs has only clique roots. Here, we generalize their result by showing that the class of $K_4$-free chordal graphs has also only clique roots. Moreover, we show that this class has always a clique root $-1$. We finally conclude the paper with several important questions and conjectures.
