Geodesic
Near threshold graphs
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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A conjecture of Grone and Merris states that for any graph $G$, its Laplacian spectrum, $\Lambda(G)$, is majorized by its conjugate degree sequence, $D^*(G)$. That conjecture prompts an investigation of the relationship between $\Lambda(G)$ and $D^*(G),$ and Merris has characterized the graphs $G$ for which the multisets $\Lambda(G)$ and $D^*(G)$ are equal. In this paper, we provide a constructive characterization of the graphs $G$ for which $\Lambda(G)$ and $D^*(G)$ share all but two elements.
DOI : 10.37236/131
Classification : 05C50, 15A18 
@article{10_37236_131,
     author = {Steve Kirkland},
     title = {Near threshold graphs},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/131},
     zbl = {1165.05331},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/131/}
}
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Steve Kirkland. Near threshold graphs. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/131

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