Disproof of a conjecture on the existence of the path-recursive period for a connected graph Original Research Article

A sufficient and necessary condition on the existence of the path-recursive period for a graph has been established in this paper. This disproves the conjecture proposed in [R. Shi, Path polynomials of a graph, Linear Algebra Appl. 236 (1996) 181–187]. Some results presented in [R. Shi, Path polynomials of a graph, Linear Algebra Appl. 236 (1996) 181–187; R.B. Bapat, A.K. Lal, Path-positive graphs, Linear Algebra Appl. 149 (1991) 125–149] have also been included.