Walks, Paths and Connectivity · Challenge problem

The Petersen graph has vertices $1,\ldots,10$: an outer $5$-cycle on $1,\ldots,5$, an inner $5$-cycle $6,8,10,7,9,6$ (each inner vertex joined to the one two steps around), and a spoke joining each $i$ to $i+5$. Find $\kappa(G) + \lambda(G)$.