Coronae graphs and their \(\alpha\)-eigenvalues

Let \(G_1\) and \(G_2\) be two simple connected graphs. The invariant \textit{coronal} of graph is used in order to determine the \(\alpha\)-eigenvalues of four different types of graph equations that are \(G_1 \circ G_2, G_1\lozenge G_1\) and the other two`s are \(G_1 \odot G_2\) and \(G_1 \circled...

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Bibliographic Details
Published inarXiv.org
Main Authors Muhammad Ateeq Tahir, Xiao-Dong, Zhang
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 04.08.2020
Subjects
Eigenvalues
Graphs
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Summary:Let \(G_1\) and \(G_2\) be two simple connected graphs. The invariant \textit{coronal} of graph is used in order to determine the \(\alpha\)-eigenvalues of four different types of graph equations that are \(G_1 \circ G_2, G_1\lozenge G_1\) and the other two`s are \(G_1 \odot G_2\) and \(G_1 \circleddash G_2\) which are obtained using the \(R\)-graph of \(G_1\). As an application we construct infinitely many pairs of non-isomorphic \(\alpha\)-Isospectral graph.
ISSN:2331-8422