哈密尔顿二次迭代线图的边度条件

Edge Degree Conditions for Hamiltonian 2-iterated Line Graphs

图G=(V(G),E(G))的线图L(G)是指以G的边集E(G)为顶点集且L(G)的2个顶点相邻当且仅当它们在G中有公共顶点.定义G的最小边度σ_(2)(G)=min{dG(u)+dG(v):uv∈E(G)}.对于连通图G,给出σ_(2)(G)的精确界,使得L(L(G))是哈密尔顿的(即存在支撑圈).对于每一条割边都是悬挂边的连通图H,给出σ_(2)(H)的精确界,使得L(L(H))是哈密尔顿的.

The line graph L(G)of G=(V(G),E(G))has E(G)as its vertex set,and two vertices are adjacent in L(G)if and only if the corresponding edges share a common end vertex in G.Let σ_(2)(G)=min{dG(u)+dG(v):uv∈E(G)}.A sharp bound of σ_(2)(G)for a connected graph G such that L(L(G))is Hamiltonian(i.e.,has a spanning cycle)is given.A sharp bound of σ_(2)(H)for a connected graph H in which every cut edge is a pendent edge such that L(L(H))is Hamiltonian is also given.