The pineapple graph is obtained by appending q pendant edges to a vertex of a complete graph. We prove that among connected graphs, the pineapple graph is determined by its adjacency spectrum. Moreover, we determine all disconnected graphs which are cospectral with a pineapple graph. Thus we find for which values of p and q the pineapple graph is determined by its adjacency spectrum. The main tool is a recent classification of all graphs with all but three eigenvalues equal to 0 or -1 by the third author.
|Journal||Discrete Applied Mathematics|
|Early online date||Oct 2018|
|Publication status||Published - Sep 2019|
- adjacency matrix
- cospectral graphs
- spectral characterization
- pineapple graph