Geodesic
A Spectral Characterization of the S-Clique Extension of the Triangular Graphs
Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 2, pp. 663-676

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A regular graph is co-edge regular if there exists a constant µ such that any two distinct and non-adjacent vertices have exactly µ common neighbors. In this paper, we show that for integers s ≥ 2 and n large enough, any co-edge-regular graph which is cospectral with the s-clique extension of the triangular graph T (n) is exactly the s-clique extension of the triangular graph T (n).
Keywords: co-edge-regular graph, triangular graph, s-clique extension 
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Tan, Ying-Ying; Koolen, Jack H.; Xia, Zheng-Jiang. A Spectral Characterization of the S-Clique Extension of the Triangular Graphs. Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 2, pp. 663-676. http://geodesic.mathdoc.fr/item/DMGT_2020_40_2_a18/