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Variations of the eccentricity and their properties in trees
Applied Mathematics and Computation ( IF 4 ) Pub Date : 2021-04-15 , DOI: 10.1016/j.amc.2021.126258
Ya-Hong Chen , Hua Wang , Xiao-Dong Zhang

Motivated from the study of eccentricity, center, and sum of eccentricities in graphs and trees, we introduce several new distance-based global and local functions based on the smallest distance from a vertex to some leaf (called the “uniformity” at that vertex). Some natural extremal problems on trees are considered. Then the middle parts of a tree is discussed and compared with the well-known center of a tree. The values of the global functions are also compared with the sum of eccentricities and some sharp bounds are established. Last but not the least, we show that the difference between the eccentricity and the uniformity, when considered as a local function, behaves in a very similar way as the eccentricity itself.



中文翻译:

树木的偏心率及其特性的变化

基于对图和树中的偏心率,中心和偏心率总和的研究,我们基于从顶点到某片叶子的最小距离(在该顶点处称为“均匀性”),引入了几种基于距离的全局和局部函数。 。考虑了树木上的一些自然极端问题。然后讨论了树的中间部分,并将其与树的众所周知的中心进行了比较。还将全局函数的值与离心率之和进行比较,并确定了一些尖锐的界限。最后但并非最不重要的一点是,我们表明,当将偏心率和均匀性之间的差异视为局部函数时,其行为与偏心率本身非常相似。

更新日期:2021-04-15
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