On the extremal total reciprocal edge-eccentricity of trees
On the extremal total reciprocal edge-eccentricity of trees
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DOI：
10.1016/j.jmaa.2015.07.057
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发表时间：
2015-08
影响因子：
1.3
通讯作者：
Shuchao Li;Lifang Zhao
中科院分区：
文献类型：
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作者：
Shuchao Li;Lifang Zhao
总倒边偏心率是一种新的图不变量，在结构活性/性质关系中具有巨大的潜力。该图不变量显示了相对于生物活性和物理性质的高鉴别力。如果G=（VG，EG）是一个简单连通图，则G的总反边偏心率（REE）定义为：ε e（G）=∑ uv ∈ EG（1/ε G（u）+ 1/ε G（v）），其中ε G（v）是顶点v的偏心率.本文首先引入四种边嫁接变换来研究G的反边偏心率的数学性质.利用这些优美的数学性质，我们刻画了n-顶点树在给定的图参数（如悬挂数、匹配数、控制数、直径、顶点二划分等）下的极图，并确定了树的互反边偏心率的一些精确界.
The total reciprocal edge-eccentricity is a novel graph invariant with vast potential in structure activity/property relationships. This graph invariant displays high discriminating power with respect to both biological activity and physical properties. If G=(V G, E G) is a simple connected graph, then the total reciprocal edge-eccentricity (REE) of G is defined as ξ e e (G)=∑ u v∈ E G (1/ε G (u)+ 1/ε G (v)), where ε G (v) is the eccentricity of the vertex v. In this paper we first introduced four edge-grafting transformations to study the mathematical properties of the reciprocal edge-eccentricity of G. Using these elegant mathematical properties, we characterize the extremal graphs among n-vertex trees with given graphic parameters, such as pendants, matching number, domination number, diameter, vertex bipartition, et al. Some sharp bounds on the reciprocal edge-eccentricity of trees are determined.