Abstract
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.
Original language | English |
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Pages (from-to) | 52-59 |
Journal | Discrete Applied Mathematics |
Volume | 269 |
Early online date | Oct 2018 |
DOIs | |
Publication status | Published - Sep 2019 |
Keywords
- adjacency matrix
- cospectral graphs
- spectral characterization
- pineapple graph