On Balanced Graphs

A graph \(G\) is defined to be balanced if its average degree is at least as large as the average degree of any of its subgraphs. We obtain a characterization of all balanced graphs with minimum degree one. We prove that maximal \(Q\) graphs are strictly balanced for several hereditary properties \(Q\). We also prove that a graph \(G\) is balanced if and only if its subdivision graph \(S(G)\) is balanced.