  Low amplitude is the defining characteristic of solar-like oscillations. The
space projects $Kepler$ and $CoRoT$ give us a great opportunity to successfully
detect such oscillations in numerous targets. Achievements of asteroseismology
depend on new discoveries of connections between the oscillation frequencies
and stellar properties. In the previous studies, the frequency of the maximum
amplitude and the large separation between frequencies were used for this
purpose. In the present study, we confirm that the large separation between the
frequencies has two minima at two different frequency values. These are the
signatures of the He {\small II} ionization zone, and as such have very strong
diagnostic potential. We relate these minima to fundamental stellar properties
such as mass, radius, luminosity, age and mass of convective zone. For mass,
the relation is simply based on the ratio of the frequency of minimum $\Delta
\nu$ to the frequency of maximum amplitude. These frequency comparisons can be
very precisely computed, and thus the mass and radius of a solar-like
oscillating star can be determined to high precision. We also develop a new
asteroseismic diagram which predicts structural and evolutionary properties of
stars with such data. We derive expressions for mass, radius, effective
temperature, luminosity and age in terms of purely asteroseismic quantities.
For solar-like oscillating stars, we now will have five very important
asteroseismic tools (two frequencies of minimum $\Delta \nu$, the frequency of
maximum amplitude, and the large and small separations between the oscillation
frequencies) to decipher properties of stellar interior astrophysics.
