On Balanced Graphs

Abstract

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.