A linear algorithm for the Hamiltonian completion number of the line graph of a tree

Abstract Given a graph G=(V,E) , HCN(L(G)) is the minimum number of edges to be added to its line graph L(G) to make L(G) Hamiltonian. This problem is known to be NP-hard for general graphs, whereas an O (|V| 5 ) algorithm exists when G is a tree. In this paper a linear algorithm for finding HCN(L(G)) when G is a tree is proposed.