On minimum degree, leaf number, traceability and Hamiltonicity in graphs

Let G be a simple connected graph with diameter d, d≠2, minimum degree δ(G) and leaf number L(G) such that δ(G)≥12(L(G)+1). We show that G is traceable. The results, apart from providing a partial solution to a conjecture (Graffiti.pc 190) of the computer program Graffiti.pc, instructed by DeLaViña, provide a new sufficient condition for traceability in graphs. In addition, we provide a family of graphs to show that the results are the best and for δ(G)≥9, we deduce that G is Hamiltonian.