Aα-Spectrum of a Firefly Graph
Let G be a connected graph of order n, A(G) is the adjacency matrix of G and D(G) is the diagonal matrix of the row-sums of A(G). In 2017, Nikiforov [Nikiforov, V., Merging the A- and Q-Spectral Theories, Applicable Analysis and Discrete Mathematics 11 (2017), pp. 81–107.] defined the convex linear...
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| Published in | Electronic notes in theoretical computer science Vol. 346; pp. 209 - 219 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
30.08.2019
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1571-0661 1571-0661 |
| DOI | 10.1016/j.entcs.2019.08.019 |
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| Abstract | Let G be a connected graph of order n, A(G) is the adjacency matrix of G and D(G) is the diagonal matrix of the row-sums of A(G). In 2017, Nikiforov [Nikiforov, V., Merging the A- and Q-Spectral Theories, Applicable Analysis and Discrete Mathematics 11 (2017), pp. 81–107.] defined the convex linear combinations Aα(G) of A(G) and D(G) byAα(G)=αD(G)+(1−α)A(G),0≤α≤1. In this paper, we obtain a partial factorization of the Aα-characteristic polynomial of the firefly graph which explicitly gives some eigenvalues of the graph. |
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| AbstractList | Let G be a connected graph of order n, A(G) is the adjacency matrix of G and D(G) is the diagonal matrix of the row-sums of A(G). In 2017, Nikiforov [Nikiforov, V., Merging the A- and Q-Spectral Theories, Applicable Analysis and Discrete Mathematics 11 (2017), pp. 81–107.] defined the convex linear combinations Aα(G) of A(G) and D(G) byAα(G)=αD(G)+(1−α)A(G),0≤α≤1. In this paper, we obtain a partial factorization of the Aα-characteristic polynomial of the firefly graph which explicitly gives some eigenvalues of the graph. |
| Author | Oliveira, Carla Silva França, Francisca Andrea Macedo Brondani, André Ebling de Lima, Leonardo |
| Author_xml | – sequence: 1 givenname: André Ebling surname: Brondani fullname: Brondani, André Ebling email: andrebrondani@id.uff.br organization: Department of Mathematics, Fluminense Federal University, Rio de Janeiro, Brazil – sequence: 2 givenname: Carla Silva surname: Oliveira fullname: Oliveira, Carla Silva email: carla.oliveira@ibge.gov.br organization: Department of Mathematics, National School of Statistics Sciences, Rio de Janeiro, Brazil – sequence: 3 givenname: Francisca Andrea Macedo surname: França fullname: França, Francisca Andrea Macedo email: francisca_franca@id.uff.br organization: Department of Mathematics, Fluminense Federal University, Rio de Janeiro, Brazil – sequence: 4 givenname: Leonardo surname: de Lima fullname: de Lima, Leonardo email: leonardo.lima@cefet-rj.br organization: Department of Production Engineering, Federal Center of Technological Education Celso Suckow da Fonseca, Rio de Janeiro, Brazil |
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| GroupedDBID | --M 0R~ 0SF 1B1 1~5 457 4G. 5GY 6I. 7-5 71M AABNK AACTN AAEDT AAEDW AAFTH AAIKJ AAKOC AALRI AAXUO ABMAC ACDAQ ACGFO ACGFS ACRLP ACXMD ADBBV ADEZE AEKER AEXQZ AFTJW AGHFR AIEXJ AIKHN AITUG AJMQA ALMA_UNASSIGNED_HOLDINGS AMRAJ AOUOD AXJTR CS3 DU5 EBS EJD EO8 EO9 EP2 EP3 FDB FEDTE FNPLU G-Q GBLVA HVGLF IHE IXB J1W KOM KQ8 M41 M~E N9A NCXOZ O-L O9- OK1 OZT P2P ROL RPZ SDF SDG SES SPC SSV SSW SSZ |
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| Keywords | Eigenvalues Aα matrix firefly Graphs |
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| References | Hong (br0040) 1986; 1 Li, Zhang (br0060) 2012; 436 Fan, Wang, Gao (br0020) 2008; 429 Hong, You (br0030) 2014; 3 Medina, Noyer, Raynaud (br0070) 2006; 27 Horn, Johnson (br0050) 1992 Nikiforov (br0080) 2017; 11 Aouchiche, Hansen, Lucas (br0010) 2011; 435 Petrović, Aleksić, Simić (br0090) 2011; 435 |
| References_xml | – volume: 435 start-page: 2591 year: 2011 end-page: 2606 ident: br0010 article-title: On the extremal values of the second largest Q-eigenvalue publication-title: Linear Algebra and its Applications – volume: 435 start-page: 2357 year: 2011 end-page: 2364 ident: br0090 article-title: On the least eigenvalue of cacti publication-title: Linear Algebra and its Applications – volume: 11 start-page: 81 year: 2017 end-page: 107 ident: br0080 article-title: Merging the A- and Q-Spectral Theories publication-title: Applicable Analysis and Discrete Mathematics – volume: 429 start-page: 577 year: 2008 end-page: 588 ident: br0020 article-title: Minimizing the least eigenvalues of unicyclic graphs with application to spectral spread publication-title: Linear Algebra and its Applications – volume: 3 start-page: 1 year: 2014 end-page: 9 ident: br0030 article-title: On the eigenvalues of firefly graphs publication-title: Transactions on Combinatorics – volume: 1 start-page: 31 year: 1986 end-page: 34 ident: br0040 article-title: Bounds on the spectra of unicyclic graphs publication-title: J. East China Norm. Univ. Natur. Sci. Ed. – volume: 436 start-page: 4400 year: 2012 end-page: 4411 ident: br0060 article-title: On the signless laplacian index of cacti with a given number of pendant vertices publication-title: Linear Algebra and its Applications – year: 1992 ident: br0050 article-title: Matrix Analysis – volume: 27 start-page: 87 year: 2006 end-page: 89 ident: br0070 article-title: Twins vertices in hypergraphs publication-title: Electronic Notes in Discrete Mathematics |
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| Snippet | Let G be a connected graph of order n, A(G) is the adjacency matrix of G and D(G) is the diagonal matrix of the row-sums of A(G). In 2017, Nikiforov... |
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| Title | Aα-Spectrum of a Firefly Graph |
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