Some Properties Of Line Graphs

In this thesis , we mainly talk about the properties of hamiltonian index and like indices in graph, and subpancyclicity in line graph. we have the following results(1) Let G be a connected graph, G′=G| (i≤2k+3)C i.If h ( G )≥k≥2, and h (G′)≥k( k∈Z),then h (G ) = h(G′).(2) If G is a graph which contains a 2-factor with k ( k≥2)cycles, then L (G ) also contains a 2-factor with k cycles.(3) If G is a graph which is vertexpancyclic ordered, then L (G ) also is vertexpancyclic ordered.(4) If G contains two edge-disjoint hamiltonian cycles, then L (G ) also contains two edge-disjoint hamiltonian cycles.(5) If G is 1-hamiltonian, then L (G ) also is 1-hamiltonian.(6) If G is a graph which is panconnected, then L (G ) also is panconnected.(7) Let G be a simple graph with n ( n≥72) vertices which satisfices condition of q1 (G )≥8.If g (G )≥5, q 2 (G )> 2 2 n + 1, then L (G ) is a subpancyclic graph and the bound of 2 2 n + 1 is the best possible .(8) Let G be a simple graph with n ( n≥72) vertices which satisfices condition of q1 (G )≥8.If g (G )≥4, q 22 (G ) ? 2 q2 (G )> 8n , then L (G ) is a subpancyclic graph and the bound of 8n is the best possible .