设G是连通图,G的k阶幂图Gk与G的顶点集相同且Gk中的两个顶点相邻当且仅当这两个顶点在G中的距离不大于k,本文给出了圈的幂图Cnk的点连通度κ(Cnk),边连通度λ(Cnk)和限制边连通度λ2(Cnk)。我们得到当1≤k⌊ n2⌋时,κ(Cnk)=λ(Cnk)=2k。关于限制边连通度,当n≥4时,λ2(Cnk)=2λ(Cnk)−2。Let G be a connected graph. The kth power Gkof G is a graph having the same vertex set of G such that the two vertices in Gkare adjacent if and only if the distance between the two vertices in G is less than or equal to k. In this paper, the connectivity κ(Cnk), edge connectivity λ(Cnk)and restricted edge connectivity λ2(Cnk)of Cnkare studied. We obtain the following results: κ(Cnk)=λ(Cnk)=2kwhen 1≤k⌊ n2⌋;λ2(Cnk)=2λ(Cnk)−2when n≥4.
在课堂教学中,采用有趣的教学内容引入方式能够有效激发学生的学习兴趣,明确教学目标,并提高课堂教学效率。本文以斐波那契序列的教学为例探索了游戏引入的方法在课堂教学中的作用。我们首先以数学游戏的方式引出斐波那契数列的概念,并分析了其在近似计算中的应用。游戏引入加应用探索的方式成功激发了学生的学习兴趣,并加强了学生对知识的理解程度和应用能力。In classroom teaching, employing engaging methods to introduce course content can effectively stimulate students’ interest in learning, clarify teaching objectives, and enhance the efficiency of classroom instruction. This paper takes the teaching of the Fibonacci sequence as an example to explore the role of game-based introductions in classroom teaching. We initially introduce the concept of the Fibonacci sequence through mathematical games and analyze its application in approximate calculations. The approach of combining game introduction with application exploration successfully ignited students’ interest in learning and strengthened their understanding and application abilities regarding the knowledge.
