Distance-unbalancedness of graphs (2011.01635v1)

Abstract: In this paper we propose and study a new structural invariant for graphs, called distance-unbalanced-ness, as a measure of how much a graph is (un)balanced in terms of distances. Explicit formulas are presented for several classes of well-known graphs. Distance-unbalancedness of trees is also studied. A few conjectures are stated and some open problems are proposed.