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).

Keywords

• co-edge-regular graph
• s-clique extension
• triangular graph
• 05c50
• 05c75
• 05c62