A note on the largest eigenvalue of non-regular graphs
A note on the largest eigenvalue of non-regular graphs
The spectral radius of connected non-regular graphs is considered. Let λ1 be the largest eigenvalue of the adjacency matrix of a graph G on n vertices with maximum degree Δ. By studying the λ1-extremal graphs, it is proved that if G is non-regular and connected, then Δ − λ1 > …