  We calculate the $F/D$ ratios of spin-nonflip baryon vertex for an arbitrary
number of color degrees of freedom $N_c$ both in the non-relativistic quark
model with the $SU(6)$ spin-flavor symmetry and in the chiral soliton model
with $SU(3)$ flavor symmetry. We find that the spin-nonflip $F/D$ ratio tends
to $-1$ in the limit of $N_c \to \infty$. We show that this leading value $F/D=
-1$ of spin-nonflip baryon vertex in the $1/N_c$ expansion corresponds to the
isoscalar dominance while the well known leading value $F/D=1/3$ of the
spin-flip vertex corresponds to the isovector dominance. We discuss origins of
the dominance of isovector in spin-flip and isoscalar in spin-nonflip baryon
vertices, referred to as the $I=J$ rule. \par In terms of the matrix elements
of the operator which transform as the generator $\lambda^8$ of the $SU(3)$
symmetry we derive the model independent isoscalar formula for baryon vertices
and apply this to the mass formula and the isoscalar part of the baryon
magnetic moments. The same Okubo-Gell-Mann mass relation and its refined
relation among the octet baryons as the one for the case $N_c=3$ is derived
model independently for arbitrary color degrees of freedom $N_c$. Contrary to
$\lambda^8$,
