The Extremal Permanental Sum for a Quasi-Tree Graph

Tingzeng Wu and Huazhong Lü

Complexity, 2019, vol. 2019, 1-4

Abstract:

Let be a graph and the adjacency matrix of . The permanent of matrix is called the permanental polynomial of . The permanental sum of is the sum of the absolute values of the coefficients of permanental polynomial of . Computing the permanental sum is #p-complete. In this note, we prove the maximum value and the minimum value of permanental sum of quasi-tree graphs. And the corresponding extremal graphs are also determined. Furthermore,we also determine the graphs with the minimum permanental sum among quasi-tree graphs of order and size , where .

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:4387650

DOI: 10.1155/2019/4387650

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