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On the Signed Complete Graphs with Maximum Index
Iranian Journal of Science and Technology, Transactions A: Science ( IF 1.7 ) Pub Date : 2021-08-26 , DOI: 10.1007/s40995-021-01199-w
Navid Kafai 1 , Farideh Heydari 1 , Mohammad Maghasedi 1 , Nader Jafari Rad 2
Affiliation  

Let \(\Gamma =(K_{n},H^-)\) be a signed complete graph whose negative edges induce a subgraph H. The index of \(\Gamma\) is the largest eigenvalue of its adjacency matrix. In this paper, we study the index of \(\Gamma\) when H is a unicyclic graph. We show that among all signed complete graphs of order \(n>5\) whose negative edges induce a unicyclic graph of order k and maximizes the index, the negative edges induce a triangle with all remaining vertices being pendant at the same vertex of the triangle.



中文翻译:

关于具有最大索引的有符号完全图

\(\Gamma =(K_{n},H^-)\)是一个有符号完全图,其负边归纳出子图H\(\Gamma\)的索引是其邻接矩阵的最大特征值。在本文中,我们研究了当H是单环图时\(\Gamma\)的索引。我们表明,在所有\(n>5\)阶有符号完全图中,其负边诱导出k阶单环图并最大化索引,负边诱导出一个三角形,所有剩余顶点都悬垂在三角形。

更新日期:2021-08-26
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