In this paper, we focus on the index (largest eigenvalue) of the adjacency matrix of connected signed graphs. We give some general results on the index when the corresponding signed graph is perturbed. As applications, we determine the first five largest indices among all unbalanced signed bicyclic graphs on \(n\ge 36\) vertices together with the correspondingPlease provide MSC codes. For more details, if required, kindly visit http://www.ams.org/msc/. extremal signed graphs whose indices attain these values.

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关于不平衡有符号双环图的索引

在本文中，我们关注于连通符号图的邻接矩阵的索引（最大特征值）。当相应的有符号图受到扰动时，我们会在索引上给出一些一般结果。作为应用程序，我们确定\（n \ ge 36 \）顶点上所有不平衡有符号双环图中的前五个最大索引以及相应的请提供MSC代码。有关更多详细信息，如果需要，请访问http://www.ams.org/msc/。其索引达到这些值的极值符号图。