Abstract

A coloring of a graph is an assignment of colors to its vertices such that adjacent vertices have different colors. Two colorings are equivalent if they induce the same partition of the vertex set into color classes. We study the average number A ( G ) of colors in the non-equivalent colorings of a graph G . We conjecture several lower bounds on A ( G ) , determine the value of this graph invariant for some classes of graphs and give general properties of A ( G ) which we will use for proving the validity of the conjectures for specific families of graphs, namely chordal graphs and graphs with maximum degree at most 2.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.