外围度量的极值界限

IF 1 Q1 MATHEMATICS Discrete Mathematics Letters Pub Date : 2023-06-27 DOI:10.47443/dml.2023.148
L. Tang
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引用次数: 0

摘要

我们研究了网络中顶点和边的几种外围度量。我们改进了在 $n$ 顶点图中,边外围性、边外围性总和以及 Trinajsti\'c 指数所达到的最大值的渐进约束。我们还证明了关于 $n$ 顶点双方形图、树和具有固定直径的图的最大值的类似结果。最后,我们反驳了 Furtula 的两个猜想,第一个是关于 Trinajsti\'c index 最小化的必要条件,第二个是关于 Trinajsti\'c index 最大化的必要条件。
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Extremal bounds on peripherality measures
We investigate several measures of peripherality for vertices and edges in networks. We improve asymptotic bounds on the maximum value achieved by edge peripherality, edge sum peripherality, and the Trinajsti\'c index over $n$ vertex graphs. We also prove similar results on the maxima over $n$-vertex bipartite graphs, trees, and graphs with a fixed diameter. Finally, we refute two conjectures of Furtula, the first on necessary conditions for minimizing the Trinajsti\'c index and the second about maximizing the Trinajsti\'c index.
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来源期刊
Discrete Mathematics Letters
Discrete Mathematics Letters Mathematics-Discrete Mathematics and Combinatorics
CiteScore
1.50
自引率
12.50%
发文量
47
审稿时长
12 weeks
期刊最新文献
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