Abstract
The inclusion graph of a finite group [Formula: see text], written as [Formula: see text], is defined to be an undirected graph that its vertices are all nontrivial subgroups of [Formula: see text], and in which two distinct subgroups [Formula: see text], [Formula: see text] are adjacent if and only if either [Formula: see text] or [Formula: see text]. In this paper, we determine the diameter of [Formula: see text] when [Formula: see text] is nilpotent, and characterize the independent dominating sets as well as the automorphism group of [Formula: see text].
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