Let

G

be a graph with

n

vertex

and A(

G

) be an adjacency matrix of a graph

G

. Then the polynomial 

π(G，x)=per(xI－A(G))

is called the permanental polynomial of

G

where

I

the unit matrix of order

n

. The permanental sum of

G

is the sum of the absolute valutes of the cofficients of

π(G，x)

. The unicyclic graphs having

I

th minimal permanental sum are determined

where

I=

3

4

5

6

7.