玫瑰窗图形的稳定性

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2024-08-05 DOI:10.1002/jgt.23162

Milad Ahanjideh, István Kovács, Klavdija Kutnar

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引用次数: 0

摘要

如果图的直积与图同构，则称该图为稳定图；反之，则称该图为不稳定图。如果一个不稳定图不是两部分的，且没有两个顶点具有相同的邻域，则称为非两部分不稳定图。Wilson 描述了九个不稳定玫瑰窗图族，并猜想这些族包含所有非难不稳定玫瑰窗图（2008 年）。在本文中，我们证明了猜想的正确性。

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Stability of Rose Window graphs

A graph $Γ$ is said to be stable if for the direct product $Γ \times K_{2}, Aut (Γ \times K_{2})$ is isomorphic to $Aut (Γ) \times Z_{2}$ ; otherwise, it is called unstable. An unstable graph is called nontrivially unstable when it is not bipartite and no two vertices have the same neighborhood. Wilson described nine families of unstable Rose Window graphs and conjectured that these contain all nontrivially unstable Rose Window graphs (2008). In this paper we show that the conjecture is true.

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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .