Transitivity of trees
For a graph [Formula: see text], a partition [Formula: see text] of the vertex set [Formula: see text] is a transitive partition if [Formula: see text] dominates [Formula: see text] whenever [Formula: see text]. The transitivity [Formula: see text] of a graph [Formula: see text] is the maximum order of a transitive partition of [Formula: see text]. For any positive integer [Formula: see text], we characterize the smallest tree with transitivity [Formula: see text] and obtain an algorithm to determine the transitivity of any tree of finite order.
2021 ◽
Vol 2021
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pp. 1-9
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2014 ◽
Vol 13
(05)
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pp. 1350162
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2017 ◽
Vol 28
(06)
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pp. 1750034
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