On the Distance Spectra of Several Double Neighbourhood Corona Graphs 
Received:May 15, 2018 Revised:December 12, 2018 
Key Word:
corona distance spectrum double neighbourhood corona graph block matrix

Fund ProjectL:Supported by the Dalian Science and Technology Project (Grant No.2015A11GX016). 

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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:20952651.2019.03.002 
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