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Abstract
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A well-known open problem in graph theory asks whether Stanley’s
chromatic
symmetric function, a generalization of the chromatic polynomial of a graph,
distinguishes between any two nonisomorphic trees. Previous work has proven the
conjecture for a class of trees called
spiders. This paper generalizes the class of spiders to
-spiders, where normal
spiders correspond to
, and
verifies the conjecture for
.
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Keywords
graph theory, combinatorics, chromatic symmetric function
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Mathematical Subject Classification 2010
Primary: 05C05, 05C31, 05E05
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Milestones
Received: 30 March 2019
Revised: 2 August 2019
Accepted: 4 November 2019
Published: 4 February 2020
Communicated by Joel Foisy
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