完全k叉树的粘连度

The tenacity and rupture degree of the complete k-ary tree

相对于其他网络抗毁性的描述指标来说,图的粘连度是比较理想,也是比较合理的刻画参数.而完全k叉树作为重要的网络结构被广泛地应用在通信网和嵌入式系统芯片的优化设计方面.本文通过优化组合方法界定了完全k叉树的粘连度和毁裂度.从某种程度刻画了网络的抗毁性,为网络设计提供了一种客观的理论依据.完全k叉树的粘连度为1/k+1(kh+1-1),如h是奇数;1/k+1(kh+1+1),如h是偶数.完全k叉树的毁裂度为(2k-1)kh-1/2-1/k-1,如h是奇数;k h+2/2-1/k-1,如h是偶数.

Abstract： Compared with other indicators for description of network anti-destroying ability, the tenacity degree of graph is ideal and also is a reasonable characterization parameter. As an important network structure, the complete k-ary trees is widely used in optimization design of communication network and embedded system chip. This article defines the tenacity and rupture degree of complete k-ary tree in the way of optimum combination. Describe the anti-destroying ability of network and by the way provide an objective theoretical basis for network designing. The tenacity of complete k-ary trees is1k＋1（kh＋1-1）,if h is an odd number; the tenacity of completek-ary trees is1k＋1（（kh＋1-1）,if h is an even number. The rupture degree of complete k-ary trees is（2k-1）kh-12,if h is an odd number; the rupture degree of complete k-ary trees iskh＋22-1k-1,if h is an even number.