A New Lower Bound on the Spectral Radius of a Graph with a Given Average Degree

This work establishes an improved lower bound for the spectral radius of a graph given its average degree. The new bound follows from an exact solution of the fractional relaxation of the problem. Our findings lead to an affirmative answer to a conjecture by Hong (1993) for graphs with specific average degrees — as the extremal graphs that meet our bound are proven to have a minimal and maximal degree that differ by at most one.