Entropy of Symmetric Graphs [article]

Seyed Saeed Changiz Rezaei, Chris Godsil
2013 arXiv   pre-print
A graph G is called symmetric with respect to a functional F_G(P) defined on the set of all the probability distributions on its vertex set if the distribution P^* maximizing F_G(P) is uniform on V(G). Using the combinatorial definition of the entropy of a graph in terms of its vertex packing polytope and the relationship between the graph entropy and fractional chromatic number, we prove that vertex transitive graphs are symmetric with respect to graph entropy. As the main result of this
more » ... we prove that a perfect graph is symmetric with respect to graph entropy if and only if its vertices can be covered by disjoint copies of its maximum-size clique. Particularly, this means that a bipartite graph is symmetric with respect to graph entropy if and only if it has a perfect matching.
arXiv:1311.6561v1 fatcat:7y6wotqinfh63gdvpplzu34yga