代数图的cop数和弱Meyniel猜想

IF 0.9 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics Pub Date : 2025-05-13 DOI:10.1016/j.ejc.2025.104168

Arindam Biswas , Jyoti Prakash Saha

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引用次数: 0

摘要

我们证明了有限群G关于对称子集S的Cayley和图的cop数，当图是连通无向的时，最多是它的两倍度。我们还证明了广义Cayley图和扭曲Cayley和图的cop数在某些条件下存在一个相似的界。这些将Frankl的结果推广到这样的图中。利用上述界和Bollobás-Janson-Riordan的结果，我们证明了弱Meyniel猜想对这些代数图成立。

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On the cop number and the weak Meyniel conjecture for algebraic graphs

We show that the cop number of the Cayley sum graph of a finite group

G

with respect to a symmetric subset

S

is at most twice its degree when the graph is connected, undirected. We also prove that a similar bound holds for the cop number of generalised Cayley graphs and twisted Cayley sum graphs under some conditions. These extend a result of Frankl to such graphs. Using the above bounds and a result of Bollobás–Janson–Riordan, we show that the weak Meyniel conjecture holds for these algebraic graphs.

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来源期刊

European Journal of Combinatorics 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.