For given graphs G1 and G2

the 2-color Ramsey number R（G1

G2） is defined to be the least positive integer p such that every 2-coloring of the edges of complete graph Kp contains a monochromatic copy of Gi colored with i

for some 1≤i≤2.We obtained some exact values by computer

M（C6）=10

M（P6）=300

M（P7）=720.When the computation complexity is high for exact values

we computed some upper bounds of Ramsey multiplicities by simulated annealing method:M（B4）≤51

M（K2

4）≤24

M（K3

3）≤150

M（K2

5）≤47

M（W6）≤34

M（B5）≤48.