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The permanental sum of a graph  G  can be defined as the sum of absolute value of coefficients of permanental polynomial of  G . It is closely related to stability of structure of a graph, and its computing complexity is #P-complete. Pentagon-chain polymers is an important type of organic polymers. In this paper, we determine the upper and lower bounds of permanental sum of pentagon-chain polymers, and the corresponding pentagon-chain polymers are also determined.

The extremal pentagon-chain polymers with respect to permanental sum