Geodesic
On co-edge-regular graphs with \(4\) distinct eigenvalues
The electronic journal of combinatorics, Tome 32 (2025) no. 3
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Tan et al. conjectured that connected co-edge-regular graphs with four distinct eigenvalues and fixed smallest eigenvalue, when having sufficiently large valency, belong to two different families of graphs. In this paper we construct two new infinite families of connected co-edge-regular graphs with four distinct eigenvalues and fixed smallest eigenvalue, thereby disproving their conjecture. Moreover, one of these constructions demonstrates that clique-extensions of Latin Square graphs are not determined by their spectrum.
DOI : 10.37236/13958
Classification : 05C50, 05B15
Mots-clés : co-edge-regular graph, s-clique extension, triangular graph 
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     author = {Hong-Jun Ge and Jack H. Koolen},
     title = {On co-edge-regular graphs with \(4\) distinct eigenvalues},
     journal = {The electronic journal of combinatorics},
     year = {2025},
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     number = {3},
     doi = {10.37236/13958},
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Hong-Jun Ge; Jack H. Koolen. On co-edge-regular graphs with \(4\) distinct eigenvalues. The electronic journal of combinatorics, Tome 32 (2025) no. 3. doi: 10.37236/13958

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