Geodesic
On adjacency and Laplacian cospectral non-isomorphic signed graphs
Ars Mathematica Contemporanea, Tome 23 (2023) no. 3, article no. 09, 20 p.

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Let Γ = (G,σ) be a signed graph, where σ is the sign function on the edges of G. In this paper, we use the operation of partial transpose to obtain  non-isomorphic Laplacian cospectral signed graphs. We will introduce two new operations on signed graphs. These operations will establish a relationship between the adjacency spectrum of one signed graph with the Laplacian spectrum of another signed graph. As an application, these new operations  will be utilized to construct several pairs of cospectral non-isomorphic signed graphs. Finally, we construct  integral signed graphs.
DOI : 10.26493/1855-3974.2902.f01
Keywords: Signed graph, partial transpose, cospectral signed graph, Laplacian cospectral signed graph, equienergetic signed graphs, integral signed graph 
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Tahir Shamsher; Shariefuddin Pirzada; Mushtaq A. Bhat. On  adjacency and Laplacian  cospectral non-isomorphic signed graphs. Ars Mathematica Contemporanea, Tome 23 (2023) no. 3, article  no. 09, 20 p. doi : 10.26493/1855-3974.2902.f01. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2902.f01/

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