Lower Bounds and properties for the average number of colors in the non-equivalent colorings of a graph

04/29/2021

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by   Alain Hertz, et al.

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We study the average number 𝒜(G) of colors in the non-equivalent colorings of a graph G. We show some general properties of this graph invariant and determine its value for some classes of graphs. We then conjecture several lower bounds on 𝒜(G) and prove that these conjectures are true for specific classes of graphs such as triangulated graphs and graphs with maximum degree at most 2.