几类双邻接日冕图的距离谱

On the Distance Spectra of Several Double Neighbourhood Corona Graphs

中文关键词:  日冕图  距离谱  双邻接日冕图  分块矩阵

英文关键词:corona  distance spectrum  double neighbourhood corona graph  block matrix

中文摘要:

      图$G$是阶数为$n$的连通图且$D(G)$为其距离矩阵.图$G$的距离特征值是它的距离矩阵的特征值.它的距离特征值及其重数构成图$G$的距离谱.在文章中,我们对分块矩阵$D_{NC}$的特征值及其对应的特征向量进行了全面的刻画.进一步,我们给出了双邻接日冕图$G^{(S)}\bullet\{G_{1},G_{2}\}$, $G^{(Q)}\bullet\{G_{1},G_{2}\}$, $G^{(R)}\bullet\{G_{1},G_{2}\}$, $G^{(T)}\bullet\{G_{1},G_{2}\}$ 的距离矩阵的特征值及其所对应的特征向量的一个全面刻画,在这里$G$ 为完全图并且$G_{1},G_{2}$为正则图.

英文摘要:

      Let $G$ be a connected graph of order $n$ and $D(G)$ be its distance matrix. The distance eigenvalues of $G$ are the eigenvalues of its distance matrix. Its distance eigenvalues and their multiplicities constitute the distance spectrum of $G$. In this article, we give a complete description of the eigenvalues and the corresponding eigenvectors of a block matrix $D_{NC}$. Further, we give a complete description of the eigenvalues and the corresponding eigenvectors of distance matrix of double neighbourhood corona graphs $G^{(S)}\bullet\{G_{1},G_{2}\}$, $G^{(Q)}\bullet\{G_{1},G_{2}\}$, $G^{(R)}\bullet\{G_{1},G_{2}\}$, $G^{(T)}\bullet\{G_{1},G_{2}\}$, where $G$ is a complete graph and $G_{1}$, $G_{2}$ are regular graphs.