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).
Author NameAffiliation
Xiaojing XU Department of Mathematics, Dalian Maritime University, Liaoning 116026, P. R. China 
Zhiping WANG Department of Mathematics, Dalian Maritime University, Liaoning 116026, P. R. China 
Jiaxue XU Department of Mathematics, Dalian Maritime University, Liaoning 116026, P. R. China 
Hits: 210
Download times: 226
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  Download reader