Energy and Randić energy of special graphs

Author
T. K., Jahfar

A. V., Chithra

Full text
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4616
10.22199/issn.0717-6279-4616
Abstract
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.
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