A natural unit interval graph on the ordered vertices ![[n]](/images/equations/NaturalUnitIntervalGraph/Inline1.svg)
is a graph specified by weakly increasing integers 
,
..., 
with 
,
having edges 
exactly when 
. The specified ordering of the vertices
is part of this convention. For 
the graph has no edges,
while 
gives the complete graph. Choosing 
gives a path graph.
Its chromatic quasisymmetric function
is symmetric in the color variables, and its elementary
expansion is the subject of the Shareshian-Wachs
conjecture.
Natural Unit Interval Graph
See also
Chromatic Quasisymmetric Function, Shareshian-Wachs ConjectureExplore with Wolfram|Alpha
References
Shareshian, J. and Wachs, M. L. "Chromatic Quasisymmetric Functions." Adv. Math. 295, 497-551, 2016. https://doi.org/10.1016/j.aim.2015.12.018.Cite this as:
Weisstein, Eric W. "Natural Unit Interval Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NaturalUnitIntervalGraph.html