Geodesic
Construction of Simultaneous Cospectral Graphs for Adjacency, Laplacian and Normalized Laplacian Matrices
Kragujevac Journal of Mathematics, Tome 47 (2023) no. 6, p. 947
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In this paper we construct several classes of non-regular graphs which are co-spectral with respect to all the three matrices, namely, adjacency, Laplacian and normalized Laplacian, and hence we answer a question asked by Butler \cite{But1}. We make these constructions starting with two pairs ($G_{1}$, $H_{1}$) and ($G_{2}$, $H_{2}$) of $A$-cospectral regular graphs, then considering the subdivision graphs $S(G_{i})$ and R-graphs $\mathcal{R}(H_{i})$, $i=1,2$, and finally making some kind of partial joins between $S(G_{1})$ and $\mathcal{R}(G_{2})$ and $S(H_{1})$ and $\mathcal{R}(H_{2})$. Moreover, we determine the number of spanning trees and the Kirchhoff index of the newly constructed graphs.
Classification : 05C50
Keywords: Adjacency matrix, Laplacian matrix, normalized Laplacian matrix, cospectral graphs 
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     author = {Arpita Das and Pratima Panigrahi},
     title = {Construction of {Simultaneous} {Cospectral} {Graphs} for {Adjacency,} {Laplacian} and {Normalized} {Laplacian} {Matrices}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {947 },
     year = {2023},
     volume = {47},
     number = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2023_47_6_a8/}
}
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Arpita Das; Pratima Panigrahi. Construction of Simultaneous Cospectral Graphs for Adjacency, Laplacian and Normalized Laplacian Matrices. Kragujevac Journal of Mathematics, Tome 47 (2023) no. 6, p. 947 . http://geodesic.mathdoc.fr/item/KJM_2023_47_6_a8/