Graphs with cyclomatic number two having panconnected square

The square of a graph G is the graph obtained from G by adding edges joining those pairs of vertices whose distance from each other in G is two. If G is connected, then the cyclomatic number of G is defined as | E ( G ) | − | V ( G ) | + 1 . Graphs with cyclomatic number no more than one whose square is Hamilton-connected have been characterized, among other things, in Chia et al. (2009) [3]. Here, we characterize all graphs G with cyclomatic number two whose square is Hamilton-connected.