Geodesic
The spectrum of neighborhood corona of graphs
Kragujevac Journal of Mathematics, Tome 35 (2011) no. 3, p. 493
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Given two graphs $G_1$ with vertices $\{v_1,v_2,\dots,v_n\}$ and $G_2$, the neighbourhood corona, $G_1 \bigstar G_2$ is the graph obtained by taking $n$ copies of $G_2$ and for each $i$, making all vertices in the $i^{th}$ copy of $G_2$ adjacent with the neighbours of $v_i$, $i=1,2,\dots,n$. In this paper a complete description of the spectrum and eigenvectors of $G_1 \bigstar G_2$ is given when $G_2$ is regular, thus adding to the class of graphs whose spectrum is completely known.
Classification : 05C05 05C12 05C50
Keywords: Spectrum, adjacency matrix, corona of graphs 
@article{KJM_2011_35_3_a12,
     author = {Indulal Gopalapillai},
     title = {The spectrum of neighborhood corona of graphs},
     journal = {Kragujevac Journal of Mathematics},
     pages = {493 },
     year = {2011},
     volume = {35},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2011_35_3_a12/}
}
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Indulal Gopalapillai. The spectrum of neighborhood corona of graphs. Kragujevac Journal of Mathematics, Tome 35 (2011) no. 3, p. 493 . http://geodesic.mathdoc.fr/item/KJM_2011_35_3_a12/