A tree T is felicitous if there is a labelling l of its vertices with distinct integers from the set {0,1,2,…,｜E(T)｜}, so that the induced edge labelling l′ defined by l′(e)=l(u)+l(v) mod ｜E(T)｜ for eac...A tree T is felicitous if there is a labelling l of its vertices with distinct integers from the set {0,1,2,…,｜E(T)｜}, so that the induced edge labelling l′ defined by l′(e)=l(u)+l(v) mod ｜E(T)｜ for each e=uv∈E(T), assigns each edge e a different label. In this paper, we constructively proved that more classes of trees are felicitous. In the end, we gave a conjecture that every lobster tree is felicitous.展开更多
文摘A tree T is felicitous if there is a labelling l of its vertices with distinct integers from the set {0,1,2,…,｜E(T)｜}, so that the induced edge labelling l′ defined by l′(e)=l(u)+l(v) mod ｜E(T)｜ for each e=uv∈E(T), assigns each edge e a different label. In this paper, we constructively proved that more classes of trees are felicitous. In the end, we gave a conjecture that every lobster tree is felicitous.
