Stability of Rose Window graphs

Pub Date : 2024-08-05 DOI:10.1002/jgt.23162

Milad Ahanjideh, István Kovács, Klavdija Kutnar

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Abstract

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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玫瑰窗图形的稳定性

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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