On the Signed Complete Graphs with Maximum Index

2021/02/05 by Kafai, N., Heydari, F., Rad, N. Jafari +1
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2102.03308

Abstract

Let Γ=(K_n,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 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.

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