On traceable and upper traceable numbers of graphs. (Q2828858)

For a connected graph \(G\) of order \(n\) at least 2 and a linear ordering \(s\) of the vertices of \(G\), \(d(s)\) is defined to be the sum of the distances between consecutive vertices of \(s\). The traceable number \(t(G)\) and the upper traceable number \(T(G)\) are defined to be the minimum and maximum, respectively, of these numbers \(d(s)\) over all linear orderings \(s\) of the vertices of \(G\). Then, for example, \(t(G)=n-1\) means that \(G\) contains a Hamiltonian path. The author investigates two realization questions for possible values of \(t(G)\) and \(T(G)\).