The Components Of 2-factors In Line Graph

In this paper .we consider mainly on the components of 2-factors in Line Graph. In Chapter two ,the components of 2-factors of the Line Graph that satisfying the Chvátal–Erd?s condition has been discussed: Let G be a graph with n vertices and if the independence number is less than or equal to the connectivity ,then L(G) has a 2-factor with k cycles forIn Chapter three and four , we consider the graphs with diameter less than two and the relation between the component of 2-factor and sum degree respectively ,we obtain:(1) Let G be a graph with n( n≥7) vertices and dia ( G )≤2 then L(G) has a 2-factor with k cycles for(2) Let G be a graph with no isolated vertices is Hamiltonian .suppose that there exist two vertices u , v∈V (G ) in G , such that d ( u ) + d ( v )≥f ( n) ,then L(G) has a 2-factor with k cycles for...