The path number of a graph
is the smallest number of edge-disjoint open paths
whose union is
(Botler et al. 2019). The same invariant is called the pathos by Harary and
Palmer (1973, p. 268).
The path number is therefore a covering invariant, not the total number of graph paths in .
The packing counterpart of the path number is the unpath
number.
Botler, F.; Cano, R.; and Sambinelli, M. "On Computing the Path Number of a Graph." Electron. Notes Theor. Comput. Sci.346,
185-197, 2019.Harary, F. and Palmer, E. M. "A Survey of Graphical
Enumeration Problems." In A Survey of Combinatorial Theory (Ed. J. N. Srivastava).
Amsterdam, Netherlands: North-Holland, pp. 259-275, 1973.
is the smallest number of edge-disjoint open paths
whose union is 
(Botler et al. 2019). The same invariant is called the pathos by Harary and
Palmer (1973, p. 268).
.
