论文标题
从辅助图获得的辅助图的距离矩阵上
On distance matrices of helm graphs obtained from wheel graphs with an even number of vertices
论文作者
论文摘要
令$ n \ geq 4 $。 Helm Graph $ h_n $上的$ 2N-1 $顶点是从轮子图$ W_N $获得的，通过将吊坠边缘与$ W_N $的外部周期的每个顶点相邻。假设$ n $是偶数。令$ d：= [d_ {ij}] $是$ h_n $的距离矩阵。在本文中，我们首先证明$ \ det（d）= 3（n-1）2^{n-1}。$接下来，我们找到一个矩阵$ ol $和vector $ u $，因此\ [d^{ - 1} = - \ frac {1} {1} {2} {2} {2} {2} {2} {2} {4} {4} {4} {4} {4} {3（n-1） $ $ $和$ d $的特征值。
Let $n \geq 4$. The helm graph $H_n$ on $2n-1$ vertices is obtained from the wheel graph $W_n$ by adjoining a pendant edge to each vertex of the outer cycle of $W_n$. Suppose $n$ is even. Let $D := [d_{ij}]$ be the distance matrix of $H_n$. In this paper, we first show that $\det(D) = 3(n-1)2^{n-1}.$ Next, we find a matrix $Ł$ and a vector $u$ such that \[D^{-1} = -\frac{1}{2}Ł+\frac{4}{3(n-1)}uu'.\] We also prove an interlacing property between the eigenvalues of $Ł$ and $D$.
