| On the Distance Spectra of Several Double Neighbourhood Corona Graphs |
| Received:May 15, 2018 Revised:December 12, 2018 |
| Key Words:
corona distance spectrum double neighbourhood corona graph block matrix
|
| Fund Project:Supported by the Dalian Science and Technology Project (Grant No.2015A11GX016). |
|
| Hits: 1111 |
| Download times: 878 |
| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2019.03.002 |
| View Full Text View/Add Comment |
|
|
|
