摘要
棒棒糖图Bm,n是由圈Cm上的任一个顶点和路Pn的一个1度顶点重合而得到n+m-1阶连通图。研究了棒棒糖图Bm,n的IC-着色和IC-指数,推出了它的IC-指数的一个上界,并借助计算机编程,证明了m分别为3,4,5时的几种棒棒糖图Bm,n的IC-着色和IC-指数。当m=3,n=1,2,…,6时,有M(B3,n)=5n+2;当m=4,n=1,2,…,5时,有M(B4,1)=13,M(B4,2)=21,M(B4,3)=26,M(B4,4)=34,M(B4,5)=40;当m=5,n=1,2,3,4时,有M(B5,1)=21,M(B5,2)=31,M(B5,3)=39,M(B5,4)=48。
The lollipop graph Bm,n is a connected graph obtained by identifying any vertex of a cycle Cm and a vertex of degree 1 of a path Pn . This paper studies the IC-indices and maximal IC-colorings of lollipop graphs. An upper bound of the IC-index of the lollipop graph Bm,n is obtained. By using a computer search, the IC-indices and maximal IC-colorings of several lollipop graphs Bm,n are obtained. The results are as follows：When m=3 and n=1,2,…,6 , M（B3,n）=5n＋2; When m=4 , M（B4,1）=13, M（B4,2）=21, M（B4,3）=26,M（B4,4）=34. When m=5 , M（B5,1）=21, M（B5,2）=31, M（B5,3）=39,M（B5,4）=48.
出处
《华东交通大学学报》
2014年第6期108-113,共6页
Journal of East China Jiaotong University
基金
国家自然科学基金(11171273)
国家大学生创新创业训练计划项目(201310699069)
