Estrada and L-Estrada Indices of Edge-Independent Random Graphs
Let \(G\) be a simple graph of order \(n\) with eigenvalues \(\lambda_1,\lambda_2,\cdots,\lambda_n\) and normalized Laplacian eigenvalues \(\mu_1,\mu_2,\cdots,\mu_n\). The Estrada index and normalized Laplacian Estrada index are defined as \(EE(G)=\sum_{k=1}^ne^{\lambda_k}\) and \(\mathcal{L}EE(G)=\...
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| Format: | Article |
| Language: | English |
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MDPI AG
2015-08-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/7/3/1455 |
| _version_ | 1811306699189911552 |
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| author | Yilun Shang |
| author_facet | Yilun Shang |
| author_sort | Yilun Shang |
| collection | DOAJ |
| description | Let \(G\) be a simple graph of order \(n\) with eigenvalues \(\lambda_1,\lambda_2,\cdots,\lambda_n\) and normalized Laplacian eigenvalues \(\mu_1,\mu_2,\cdots,\mu_n\). The Estrada index and normalized Laplacian Estrada index are defined as \(EE(G)=\sum_{k=1}^ne^{\lambda_k}\) and \(\mathcal{L}EE(G)=\sum_{k=1}^ne^{\mu_k-1}\), respectively. We establish upper and lower bounds to \(EE\) and \(\mathcal{L}EE\) for edge-independent random graphs, containing the classical Erdös-Rényi graphs as special cases. |
| first_indexed | 2024-04-13T08:50:09Z |
| format | Article |
| id | doaj.art-a53c112a40464109b98a8491325c8a88 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T08:50:09Z |
| publishDate | 2015-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-a53c112a40464109b98a8491325c8a882022-12-22T02:53:31ZengMDPI AGSymmetry2073-89942015-08-01731455146210.3390/sym7031455sym7031455Estrada and L-Estrada Indices of Edge-Independent Random GraphsYilun Shang0Department of Mathematics, Tongji University, Shanghai 200092, ChinaLet \(G\) be a simple graph of order \(n\) with eigenvalues \(\lambda_1,\lambda_2,\cdots,\lambda_n\) and normalized Laplacian eigenvalues \(\mu_1,\mu_2,\cdots,\mu_n\). The Estrada index and normalized Laplacian Estrada index are defined as \(EE(G)=\sum_{k=1}^ne^{\lambda_k}\) and \(\mathcal{L}EE(G)=\sum_{k=1}^ne^{\mu_k-1}\), respectively. We establish upper and lower bounds to \(EE\) and \(\mathcal{L}EE\) for edge-independent random graphs, containing the classical Erdös-Rényi graphs as special cases.http://www.mdpi.com/2073-8994/7/3/1455Estrada indexNormalized Laplacian Estrada indexedge-independent random graph |
| spellingShingle | Yilun Shang Estrada and L-Estrada Indices of Edge-Independent Random Graphs Symmetry Estrada index Normalized Laplacian Estrada index edge-independent random graph |
| title | Estrada and L-Estrada Indices of Edge-Independent Random Graphs |
| title_full | Estrada and L-Estrada Indices of Edge-Independent Random Graphs |
| title_fullStr | Estrada and L-Estrada Indices of Edge-Independent Random Graphs |
| title_full_unstemmed | Estrada and L-Estrada Indices of Edge-Independent Random Graphs |
| title_short | Estrada and L-Estrada Indices of Edge-Independent Random Graphs |
| title_sort | estrada and l estrada indices of edge independent random graphs |
| topic | Estrada index Normalized Laplacian Estrada index edge-independent random graph |
| url | http://www.mdpi.com/2073-8994/7/3/1455 |
| work_keys_str_mv | AT yilunshang estradaandlestradaindicesofedgeindependentrandomgraphs |