论文标题
在签名树的最低维纳指数上的猜想
Disproof of a conjecture on the minimum Wiener index of signed trees
论文作者
论文摘要
连接图的Wiener索引是所有未排序的顶点对之间的距离之和。 Sam Spiro [签名图的Wiener索引，应用。数学。 Comput。，416（2022）126755]最近引入了签名图的Wiener索引，并推测带有交替标志的路径$ p_n $在所有签名的树中具有最小的Wiener索引，该树具有$ N $ Vertices的所有签名树。通过构建一个无限的反示例家族，我们证明猜想至少为30 $ 30时是错误的。
The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices. Sam Spiro [The Wiener index of signed graphs, Appl. Math. Comput., 416(2022)126755] recently introduced the Wiener index for a signed graph and conjectured that the path $P_n$ with alternating signs has the minimum Wiener index among all signed trees with $n$ vertices. By constructing an infinite family of counterexamples, we prove that the conjecture is false whenever $n$ is at least 30.
