GRAPHS COSPECTRAL WITH H(3, q) WHICH ARE DISJOINT UNIONS OF AT MOST THREE COMPLETE GRAPHS

Abstract

Let a connected graph Γ be locally disjoint union of at most three complete graphs and let Γ be cospectral with the Hamming graph H(3, q) (q ≥ 2). In this paper, we show that Γ is either the Hamming graph H(3, q) or the dual graph of H(3, 3) (i.e., the graph whose vertices are the triangles of H(3, 3) and two triangles are adjacent if they intersect).