CAJ | 학술논문

文章将树做了推广，给出了圈树的定义：把树的度数大于3的若干点用相应点度数一样长的圈替换得到的图为圈树。证明了点赋权树T（权重均为正），权和为W，则存在一个点v∈V（T），使得T—v的所有连通片的权和不大于W/2。以此为基础，证明了n阶圈树D，证明了一定存在{u，v}，使D-{u，v}，所有的连通片的阶都不大于[n/2]，最后对圈树的一些特征值阶进行了估计。
문장장수주료추엄，급출료권수적정의：파수적도수대우3적약간점용상응점도수일양장적권체환득도적도위권수。증명료점부권수T（권중균위정），권화위W，칙존재일개점v∈V（T），사득T—v적소유련통편적권화불대우W/2。이차위기출，증명료n계권수D，증명료일정존재{u，v}，사D-{u，v}，소유적련통편적계도불대우[n/2]，최후대권수적일사특정치계진행료고계。
In this paper, Abstract. Let T be a tree with maximum degree at least 4. If we replace some vertex of degree k （ k 〉 3 ） of T with k --cycle, we obtain a graph called circle --trees. With each vertex u of T let there be associated a real positive number w（u） , called its weight . Then T , together with these v.eights on its vertices, is called a weighted tree . The sum of all weights on its vertices is called weight sum . In this paper, we prove that, for a weighted tree T with weight sum W, there is a vertex v of T such W that the weight sum of all components of T-- v is at most W/2 . Furthermore, we show that, for circle -- trees D with n vertices, there exist u and v of D such that the order of each components of D-- {u,v} is no more than n/2 , and then estimate some ranks of Eigenvalues of circle --trees.