Diameters and automorphism groups of inclusion graphs over nilpotent groups
2019 ◽
Vol 19
(05)
◽
pp. 2050097
Keyword(s):
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].
2019 ◽
Vol 19
(12)
◽
pp. 2150001
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1986 ◽
Vol 40
(2)
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pp. 253-260
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2011 ◽
Vol 331
(1)
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pp. 482-489
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2005 ◽
Vol 78
(3)
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pp. 429-439
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1964 ◽
Vol 16
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pp. 485-489
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1981 ◽
Vol 33
(2)
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pp. 412-420
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1979 ◽
Vol 28
(3)
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pp. 335-345
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