树木线性安排的边缘长度和边缘长度之和的边界 (Bounds of the sum of edge lengths in linear arrangements of trees)

A fundamental problem in network science is the normalization of the topological or physical distance between vertices, that requires understanding the range of variation of the unnormalized distances. Here we investigate the limits of the variation of the physical distance in linear arrangements of the vertices of trees. In particular, we investigate various problems on the sum of edge lengths in trees of a fixed size: the minimum and the maximum value of the sum for specific trees, the minimum and the maximum in classes of trees (bistar trees and caterpillar trees) and finally the minimum and the maximum for any tree. We establish some foundations for research on optimality scores for spatial networks in one dimension.

翻译：网络科学的一个根本问题是脊椎之间的表面或物理距离正常化,这需要了解非正常距离的变化范围。在这里,我们调查树木脊椎线性安排中物理距离变化的限度。特别是,我们调查固定大小树木边缘长度之和的各种问题:具体树木的最小值和最大值,树类(双星树和毛虫树)的最小值和最大值,最后是任何树木的最低值和最大值。我们为研究空间网络在一个层面的最佳度分数建立一些基础。