关于图(s〈c_4,n〉)∪P_m的优美性

The gracefulness of graph(s〈c_4,n〉)∪P_m

证明了满足一定条件的交错图G和任意m≥2的简单通路Pm的不交并图G∪Pm是优美图;进一步研究了(s〈c4,n〉)∪Pm的优美性,证明了当ni>2,ti≥1,m≥2时,图∪ri=1(2ti〈c4,ni〉)∪Pm是优美图.其中:图〈c4,n〉是将n个c4中的每一个c4的一个顶点粘接在一起得到的新图,(s〈c4,n〉)∪Pm是s个〈c4,n〉与一个Pm的不交并.

The present article proves the fact that the graph G∪Pm which is the disjoint union of an alternating graph G with given conditions and an path Pm with m≥2 edges is a graceful graph.Furthermore the article does the research on the gracefulness of(s〈c4,n〉)∪Pm,which proves that ∪ri=1(2ti〈c4,ni〉)∪Pm is graceful in case that ni>2,ti≥1,m≥2,in which the graph 〈c4,n〉 is achieved by identifying a vertex of each c4 of nc4 with one vertex and the graph(s〈c4,n〉)∪Pm is the disjoint union of s〈c4,n〉 and Pm.