Ruskey and Savage asked the following question: Does every (not necessarily perfect) matching of Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? We consi
The pentagon distance index S(F) of a fullerene graph F is defined as:S(F) =Σu,v dH(u,v), where the sum is over all vertex pairs in the dual graph H of F e
Let G be a graph of order n(G), minimum degree δ(G) and connectivity κ(G).We call the graph G maximally connected when κ(G) =δ(G).The graph G is said to
The problem on a quadratic lattice embedded on the torus is considered here.In 1991, Thomassen characterized that there only two types of quadrilateral latt