The Extremal Permanental Sum for a Quasi-Tree Graph
Let G be a graph and A(G) the adjacency matrix of G. The permanent of matrix (xI-A(G)) is called the permanental polynomial of G. The permanental sum of G is the sum of the absolute values of the coefficients of permanental polynomial of G. Computing the permanental sum is #p-complete. In this note,...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi-Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/4387650 |
| Summary: | Let G be a graph and A(G) the adjacency matrix of G. The permanent of matrix (xI-A(G)) is called the permanental polynomial of G. The permanental sum of G is the sum of the absolute values of the coefficients of permanental polynomial of G. 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 n and size m, where n-1≤m≤2n-3. |
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| ISSN: | 1076-2787 1099-0526 |