华东交通大学学报
華東交通大學學報
화동교통대학학보
JOURNAL OF EAST CHINA JIAOTONG UNIVERSITY
2014年
6期
108-113
,共6页
IC-着色%IC-指数%棒棒糖图
IC-著色%IC-指數%棒棒糖圖
IC-착색%IC-지수%봉봉당도
IC-coloring%IC-index%lollipop graphs
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。
棒棒糖圖Bm,n是由圈Cm上的任一箇頂點和路Pn的一箇1度頂點重閤而得到n+m-1階連通圖。研究瞭棒棒糖圖Bm,n的IC-著色和IC-指數,推齣瞭它的IC-指數的一箇上界,併藉助計算機編程,證明瞭m分彆為3,4,5時的幾種棒棒糖圖Bm,n的IC-著色和IC-指數。噹m=3, n=1,2,…,6時,有M(B3,n)=5n+2;噹m=4, n=1,2,…,5時,有M(B4,1)=13, M(B4,2)=21, M(B4,3)=26,M(B4,4)=34, M(B4,5)=40;噹m=5, n=1,2,3,4時,有M(B5,1)=21,M(B5,2)=31, M(B5,3)=39,M(B5,4)=48。
봉봉당도Bm,n시유권Cm상적임일개정점화로Pn적일개1도정점중합이득도n+m-1계련통도。연구료봉봉당도Bm,n적IC-착색화IC-지수,추출료타적IC-지수적일개상계,병차조계산궤편정,증명료m분별위3,4,5시적궤충봉봉당도Bm,n적IC-착색화IC-지수。당m=3, n=1,2,…,6시,유M(B3,n)=5n+2;당m=4, n=1,2,…,5시,유M(B4,1)=13, M(B4,2)=21, M(B4,3)=26,M(B4,4)=34, M(B4,5)=40;당m=5, n=1,2,3,4시,유M(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 ver?tex 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.