Geodesic
Construction of Simultaneous Cospectral Graphs for Adjacency, Laplacian and Normalized Laplacian Matrices
Kragujevac Journal of Mathematics, Tome 47 (2023) no. 6, p. 947

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 
@article{KJM_2023_47_6_a8,
     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 },
     publisher = {mathdoc},
     volume = {47},
     number = {6},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2023_47_6_a8/}
}
TY  - JOUR
AU  - Arpita Das
AU  - Pratima Panigrahi
TI  - Construction of Simultaneous Cospectral Graphs for Adjacency, Laplacian and Normalized Laplacian Matrices
JO  - Kragujevac Journal of Mathematics
PY  - 2023
SP  - 947 
VL  - 47
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KJM_2023_47_6_a8/
LA  - en
ID  - KJM_2023_47_6_a8
ER  - 
%0 Journal Article
%A Arpita Das
%A Pratima Panigrahi
%T Construction of Simultaneous Cospectral Graphs for Adjacency, Laplacian and Normalized Laplacian Matrices
%J Kragujevac Journal of Mathematics
%D 2023
%P 947 
%V 47
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KJM_2023_47_6_a8/
%G en
%F KJM_2023_47_6_a8
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/