Leaf number and Hamiltonian $$C_4$$ C 4 -free graphs

Abstract

Let G be a simple 2-connected, $$C_4$$ -free graph with minimum degree $$\delta (G)\ge 4$$ and leaf number L(G) such that $$\delta (G)\ge \displaystyle \frac{1}{2}L(G)$$ . We show that G is Hamiltonian. In addition, we provide family of graphs to show that the results are best possible for aforementioned class of graphs. The results, apart from supporting the conjecture (Graffiti.pc 190) of the computer program Graffiti.pc, instructed by DeLaVi $${\tilde{n}}$$ a, provide a new sufficient condition for Hamiltonicity in $$C_4$$ -free graphs.