On the Signed Complete Graphs with Maximum Index

N. Kafaie | F. Heydari | Nader Jafari Rad | M. Maghasedi

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URL :   http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=169866
Date :  2021/09/08
Publish in :    Iranian Journal of Science and Technology, Transactions A: Science

Link :  https://link.springer.com/article/10.1007/s40995-021-01199-w
Keywords : signed complete graph

Abstract :

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Let Γ=(Kn,H−) be a signed complete graph whose negative edges induce a subgraph H. The index of Γ is the largest eigenvalue of its adjacency matrix. In this paper, we study the index of Γ when H is a unicyclic graph. We show that among all signed complete graphs of order n5 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.