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,...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/4387650 |
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| author | Tingzeng Wu Huazhong Lü |
| author_facet | Tingzeng Wu Huazhong Lü |
| author_sort | Tingzeng Wu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-63bc16f3b0504989a0559f4013eba4e5 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-63bc16f3b0504989a0559f4013eba4e52025-02-03T01:23:20ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/43876504387650The Extremal Permanental Sum for a Quasi-Tree GraphTingzeng Wu0Huazhong Lü1School of Mathematics and Statistics, Qinghai Nationalities University, Xining, Qinghai 810007, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, ChinaLet 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.http://dx.doi.org/10.1155/2019/4387650 |
| spellingShingle | Tingzeng Wu Huazhong Lü The Extremal Permanental Sum for a Quasi-Tree Graph Complexity |
| title | The Extremal Permanental Sum for a Quasi-Tree Graph |
| title_full | The Extremal Permanental Sum for a Quasi-Tree Graph |
| title_fullStr | The Extremal Permanental Sum for a Quasi-Tree Graph |
| title_full_unstemmed | The Extremal Permanental Sum for a Quasi-Tree Graph |
| title_short | The Extremal Permanental Sum for a Quasi-Tree Graph |
| title_sort | extremal permanental sum for a quasi tree graph |
| url | http://dx.doi.org/10.1155/2019/4387650 |
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