On the Hamiltonian Index

Liming Xiong
Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P.R. China
lmxiong@eyou.com

Abstract     Full Text  PDF

Hamiltonicity of a graph is the well-studied concept. The line graph operation on graphs is also a well-studied one of operations, itrelates the concept of coloring of a graph. Harary and Nash-Williams gave a relation between the graph and its hamiltonian line graph. The hamiltonian index is the smallest number of iterations of the line graph operation that will yield a hamiltonian iterated graph. In this talk, we will present a relation between the graph and its hamiltonian iterated line graphs. We will also give a survey of the research of the hamiltonian index.