Energy and Randić energy of special graphs

In this paper, we determine the Randić energy of the m-splitting graph, the m-shadow graph and the m-duplicate graph of a given graph, m being an arbitrary integer. Our results allow the construction of an infinite sequence of graphs having the same Randić energy. Further, we determine some graph in...

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Bibliographic Details
Published in:Proyecciones (Antofagasta, Chile) Chile), 2022-08, Vol.41 (4), p.855-877
Main Authors: T. K., Jahfar, A. V., Chithra
Format: Article
Language:English
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Summary:In this paper, we determine the Randić energy of the m-splitting graph, the m-shadow graph and the m-duplicate graph of a given graph, m being an arbitrary integer. Our results allow the construction of an infinite sequence of graphs having the same Randić energy. Further, we determine some graph invariants like the degree Kirchhoff index, the Kemeny’s constant and the number of spanning trees of some special graphs. From our results, we indicate how to obtain infinitely many pairs of equienergetic graphs, Randić equienergetic graphs and also, infinite families of integral graphs.
ISSN:0717-6279
0717-6279
DOI:10.22199/issn.0717-6279-4616