Hamiltonian Indices of Three Classes of Graphs Obtained from Petersen Graph

In this paper, we mainly consider the Hamiltonian indices of three classes of graphs obtained from Petersen graph, that is, the minimum integer m of m-time iterated line graph L-m(G) of these three classes of graphs such that L-m(G) is Hamiltonian. We show that the Hamiltonian indices of those graphs obtained by replacing every vertex of Petersen graph with a n-cycle or a complete graph of order n, or adding n pendant edges to each vertex of Petersen graph are both 2. In addition, we also study the situations of adding an edge to these three classes of graphs and obtain that their Hamiltonian indices are both 2.