The e positivity of some new classes of graphs

2024/05/20 by Mitrovic, Stefan, Stojadinovic, Tanja · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.11946

Abstract

We introduce two classes of graphs - suns and dumbbells, both with few variations and explore their chromatic symmetric function and its e-positivity. We also give many connections of these two classes with other classes of connected graphs.

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• The trinacria graphs T_(b+2)b2 are e-positive

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• The chromatic symmetric function of graphs glued at a single vertex
• Chromatic Posets
• The twinning operation on graphs does not always preserve e-positivity
• Classes of graphs with e-positive chromatic symmetric function
• Chromatic symmetric functions and H-free graphs