图(s〈C_4,3〉)∪P_m的优美性

On the gracefulness of(s〈C_4,3〉)∪P_m

研究了图(s〈C4,3〉)∪Pm的优美性,证明了当s为大于等于2的自然数,m为任意正整数时,图(s〈C4,3〉)∪Pm是优美的.其中图〈C4,3〉是将3个C4中每个C4的一个顶点粘接到一起得到的新图,Pm是有m+1个顶点的路,而(s〈C4,3〉)∪Pm是s个〈C4,3〉与一个Pm的非连通并.文中所得结果部分解决了已有文献给出的猜想.

This article deals with the gracefulness of graph（s〈C4,3〉）∪Pmand proves that（s〈C4,3〉）∪Pmis graceful when s≥2（s and mare positive integer）,where the graph 〈C4,3〉is achieved by identifying a vertex of each C4 of 3C4s with one vertex,graph Pmis the path with m＋1vertexes,and graph（s〈C4,3〉）∪Pmis the disjoint union of（s〈C4,3〉）s and Pm.