Some Properties on Estrada Index of Folded Hypercubes Networks
Let G be a simple graph with n vertices and let λ1,λ2,…,λn be the eigenvalues of its adjacency matrix; the Estrada index EEG of the graph G is defined as the sum of the terms eλi, i=1,2,…,n. The n-dimensional folded hypercube networks FQn are an important and attractive variant of the n-dimensional...
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| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/167623 |
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| author | Jia-Bao Liu Xiang-Feng Pan Jinde Cao |
| author_facet | Jia-Bao Liu Xiang-Feng Pan Jinde Cao |
| author_sort | Jia-Bao Liu |
| collection | DOAJ |
| description | Let G be a simple graph with n vertices and let λ1,λ2,…,λn be the eigenvalues of its adjacency matrix; the Estrada index EEG of the graph G is defined as the sum of the terms eλi, i=1,2,…,n. The n-dimensional folded hypercube networks FQn are an important and attractive variant of the n-dimensional hypercube networks Qn, which are obtained from Qn by adding an edge between any pair of vertices complementary edges. In this paper, we establish the explicit formulae for calculating the Estrada index of the folded hypercubes networks FQn by deducing the characteristic polynomial of the adjacency matrix in spectral graph theory. Moreover, some lower and upper bounds for the Estrada index of the folded hypercubes networks FQn are proposed. |
| format | Article |
| id | doaj-art-7049a65df8f34f8d8c2111d3d8c524c7 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-7049a65df8f34f8d8c2111d3d8c524c72025-02-03T01:10:48ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/167623167623Some Properties on Estrada Index of Folded Hypercubes NetworksJia-Bao Liu0Xiang-Feng Pan1Jinde Cao2School of Mathematics Science, Anhui University, Hefei 230601, ChinaSchool of Mathematics Science, Anhui University, Hefei 230601, ChinaDepartment of Mathematics, Southeast University, Nanjing 210096, ChinaLet G be a simple graph with n vertices and let λ1,λ2,…,λn be the eigenvalues of its adjacency matrix; the Estrada index EEG of the graph G is defined as the sum of the terms eλi, i=1,2,…,n. The n-dimensional folded hypercube networks FQn are an important and attractive variant of the n-dimensional hypercube networks Qn, which are obtained from Qn by adding an edge between any pair of vertices complementary edges. In this paper, we establish the explicit formulae for calculating the Estrada index of the folded hypercubes networks FQn by deducing the characteristic polynomial of the adjacency matrix in spectral graph theory. Moreover, some lower and upper bounds for the Estrada index of the folded hypercubes networks FQn are proposed.http://dx.doi.org/10.1155/2014/167623 |
| spellingShingle | Jia-Bao Liu Xiang-Feng Pan Jinde Cao Some Properties on Estrada Index of Folded Hypercubes Networks Abstract and Applied Analysis |
| title | Some Properties on Estrada Index of Folded Hypercubes Networks |
| title_full | Some Properties on Estrada Index of Folded Hypercubes Networks |
| title_fullStr | Some Properties on Estrada Index of Folded Hypercubes Networks |
| title_full_unstemmed | Some Properties on Estrada Index of Folded Hypercubes Networks |
| title_short | Some Properties on Estrada Index of Folded Hypercubes Networks |
| title_sort | some properties on estrada index of folded hypercubes networks |
| url | http://dx.doi.org/10.1155/2014/167623 |
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