I have come across a question that requires finding the smallest spectral radius of a signed Petersen graph, i.e., find the smallest $p \geq 0$ such that there exists a signed adjacency matrix of the Petersen graph whose eigenvalues lie in the interval $[-p,p]$.
I have come across the paper Six signed Petersen graphs, and their automorphisms by Thomas Zaslavsky. Even though I can generate the spectral radius for the 6 equivalence classes, is there a shorter way to find it algebraically?