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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Bibliographic Details
Published inElectronic notes in theoretical computer science Vol. 346; pp. 209 - 219
Main Authors Brondani, André Ebling, Oliveira, Carla Silva, França, Francisca Andrea Macedo, de Lima, Leonardo
Format Journal Article
LanguageEnglish
Published Elsevier B.V 30.08.2019
Subjects
Aα matrix
Eigenvalues
firefly Graphs
Eigenvalues
Aα matrix
firefly Graphs
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ISSN1571-0661
1571-0661
DOI10.1016/j.entcs.2019.08.019

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Summary: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.
ISSN:1571-0661
1571-0661
DOI:10.1016/j.entcs.2019.08.019