On the common-neighborhood energy of a graph (Q2853216)
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scientific article; zbMATH DE number 6217170
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the common-neighborhood energy of a graph |
scientific article; zbMATH DE number 6217170 |
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18 October 2013
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graph spectra
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graph energy
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common neighborhood
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strongly regular graphs
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0.8960606
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On the common-neighborhood energy of a graph (English)
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The common-neighborhood matrix \(\mathrm{CN}\) of a graph \(G\) displays at position \((i,j)\) the number of common neighbors for vertices \(i\) and \(j\). The common-neighborhood energy \(E_{\mathrm{CN}}\) of \(G\) is equal to the sum of absolute values of eigenvalues of CN. The authors obtain an upper bound for \(E_{\mathrm{CN}}\) when \(G\) is strongly regular. It is also shown that \(E_{\mathrm{CN}}\) of several classes of graphs is less than the common-neighborhood energy of the complete graph \(K_n\).
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