【摘要】 对于简单图G=<V,E>,如果存在一个映射f:V(G)→{0,1,2,…,|E|+k-1}满足:1)对任意的u,v∈V,若u≠v,则f(u)≠f(v);2)max{f(u)|u∈V}=|E|+k-1;3)对任意的e1,e2∈E,若e1≠e2,则g(e1)≠g(e2),且{g(e1)|e∈E}={k,k+1,…,|E|+k-1},g(e2)=|f(u)-f(v)|,e=uv,则称G是k-优美图,f称为G的k-优美标号.作者研究了一类图的k-优美标号.更多还原

【Abstract】 Let G=<V,E>was a simple graph.If there exists a mapping f:V(G)→{0,1,2,…,|E|+k-1} satisfied: 1)u,v∈V,u≠v,f(u)≠f(v);2)max{f(u)|u∈V}=|E|+k-1;3)e1,e2∈E,e1≠e2,g(e1)≠g(e2),and{g(e)|e∈E}={k,k+1,…,|E|+k-1},where g(e)=|f(u)-f(v)|,e=uv,the G is called k-graceful graph,and f is called k-graceful labeling.In this paper,we prove that graph P2r,2s-1 are k-graceful graphs.更多还原