Some results on inversity of endomorphism monoid of generalized join

The property of endomorphism of the generalized join is discussed. The following result are obtained: let G = Gejo(X, Y; y1, y2,…, ym) be a generalized join. Suppose X has no isolated vertex, Y has no K3-subgraph, Z is a set composed of all vertices in V/Y\\{y1, y2,…, ym} which are adjacent to at least one joint-vertex in Y, and y∈Z dY\\{y1,y2,…,ym}(y) = 0- (1) When G is inverse, so is Y1= Y{y1, y2,…, ym}; (2) When G is inverse and d(y)≤2, then X + Y1 is also inverse.