二部图和分裂图的Mostar指数最大化

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED Discrete Optimization Pub Date : 2023-05-01 DOI:10.1016/j.disopt.2023.100768

Štefko Miklavič , Johannes Pardey , Dieter Rautenbach , Florian Werner

引用次数: 4

摘要

Došlić等人。定义图G的Mostar指数为∑uv∈E（G）|nG（u，v）−nG（v，u）|，其中，对于G的边uv，项nG（u，v）表示G的顶点数，这些顶点在G中与u的距离小于与v的距离。，我们证明了n阶二部图的Mostar指数至多为318n3，n阶分裂图的Mosstar指数至多为427n3。

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Maximizing the Mostar index for bipartite graphs and split graphs

Došlić et al. defined the Mostar index of a graph $G$ as $\sum_{u v \in E (G)} | n_{G} (u, v) - n_{G} (v, u) |$ , where, for an edge $u v$ of $G$ , the term $n_{G} (u, v)$ denotes the number of vertices of $G$ that have a smaller distance in $G$ to $u$ than to $v$ . Contributing to conjectures posed by Došlić et al., we show that the Mostar index of bipartite graphs of order $n$ is at most $\frac{\sqrt{3}}{18} n^{3}$ , and that the Mostar index of split graphs of order $n$ is at most $\frac{4}{27} n^{3}$ .

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来源期刊

Discrete Optimization 管理科学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.

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