A Spectral Characterization of the S-Clique Extension of the Triangular Graphs

Abstract 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).

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