Diameters and automorphism groups of inclusion graphs over nilpotent groups

摘要

The inclusion graph of a finite group G, written as In(G), is defined to be an undirected graph that its vertices are all nontrivial subgroups of G, and in which two distinct. subgroups H, K are adjacent if and only if either H subset of K or K subset of H. In this paper, we determine the diameter of In(G) when G is nilpotent, and characterize the independent dominating sets as well as the automorphism group of In(Z(n)).