Merrifield-Simmons猜想对二部图成立
The Merrifield-Simmons conjecture holds for bipartite graphs
摘要：
设$G = (V, E)$是一个图，$σ(G)$是$G$中独立顶点集的个数.然后Merrifield-Simmons猜想指出，项$σ(G_{-u}) \cdot σ(G_{-v}) - σ(G) \cdot σ(G_{-u-v})$的符号仅取决于$G$中的顶点$u, v \in V$的距离的奇偶性。我们证明了猜想成立的二部图考虑一个推广的术语，其中顶点子集，而不是顶点被删除。
英文摘要：
Let $G = (V, E)$ be a graph and $σ(G)$ the number of independent (vertex) sets in $G$. Then the Merrifield-Simmons conjecture states that the sign of the term $σ(G_{-u}) \cdot σ(G_{-v}) - σ(G) \cdot σ(G_{-u-v})$ only depends on the parity of the distance of the vertices $u, v \in V$ in $G$. We prove that the conjecture holds for bipartite graphs by considering a generalization of the term, where vertex subsets instead of vertices are deleted.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
