ADV MATH SCI JOURNAL Advances in Mathematics: Scientific Journal 10 (2021), no.3, 1259–1271 ISSN: 1857-8365 (printed); 1857-8438 (electronic) https://doi.org/10.37418/amsj.10.3.14 ON LAPLACIAN SPECTRA OF SOME CORONA PRODUCT GRAPHS AND APPLICATIONS Idweep J. Gogoi, Bablee Phukan, Aditya Pegu, and A. Bharali 1 ABSTRACT. The corona operations on graphs have attracted many researchers because of its applications in various fields. Many variants of the corona op- eration are defined over the years and their spectral properties have also been studied. In this paper we consider the spectra of some of these corona graphs namely; weighted edge corona product graphs, subdivision double corona, Q- graph double corona and total double corona. In this note, we correct some of the results proposed in the literature and also derive expressions for the num- ber of spanning trees and Kirchhoff index of the above mentioned graphs as applications. 1. I NTRODUCTION We consider simple and connected graphs throughout this paper. For a graph G =(V,E) with vertex set V (G)= {v 1 ,v 2 ,...,v n } and edge set E(G)= {e 1 ,e 2 , ...,e m }, the Laplacian matrix is defined as L(G)= D(G) − A(G). Here D(G) is the diagonal matrix with diagonal entries as the degrees of the vertices of G 1 corresponding author 2020 Mathematics Subject Classification. 05C50, 05C90, 15A18. Key words and phrases. corona, double corona, weighted edge corona network, spanning trees, Kirchhoff index. Submitted: 21.02.2021; Accepted: 11.03.2021; Published: 16.03.2021. 1259