Maximizing the index of signed complete graphs with spanning trees on $k$ pendant vertices

Dan Li, Minghui Yan, Zhaolin Teng

A signed graph $\Sigma =(G,\sigma )$ consists of an underlying graph $G=(V,E)$ with a sign function $\sigma :E\to \{-1,1\}$. Let $A(\Sigma )$ be the adjacency matrix of $\Sigma$ and ${\lambda }_1(\Sigma )$ denote the…