  A Gallai $k$-coloring is a $k$-edge coloring of a complete graph in which
there are no rainbow triangles. For given graphs $G_1, G_2, G_3$ and
nonnegative integers $r, s, t$ with that $k=r+s+t$, the $k$-colored
Gallai-Ramsey number $gr_{k}(K_{3}: r\cdot G_1,~ s\cdot G_2, ~t\cdot G_3)$ is
the minimum integer $n$ such that every Gallai $k$-colored $K_{n}$ contains a
monochromatic copy of $G_1$ colored by one of the first $r$ colors or a
monochromatic copy of $G_2$ colored by one of the middle $s$ colors or a
monochromatic copy of $G_3$ colored by one of the last $t$ colors. In this
paper, we determine the value of Gallai-Ramsey number in the case that
$G_1=B_{3}^{+}$, $G_2=S_{3}^+$ and $G_3=K_3$. Then the Gallai-Ramsey number
$gr_{k}(K_{3}: B_{3}^{+})$ is obtained. Thus the Gllai-Ramsey numbers for
graphs with five vertices and eight edges are solved completely. Furthermore,
the the Gallai-Ramsey numbers $gr_{k}(K_{3}: r\cdot B_3^+,~ (k-r)\cdot S_3^+)$,
$gr_{k}(K_{3}: r\cdot B_3^+,~ (k-r)\cdot K_3)$ and $gr_{k}(K_{3}: s\cdot
S_3^+,~ (k-s)\cdot K_3)$ are obtained, respecticely.
