Geodesic
Graphs with at most Four Seidel Eigenvalues
Kragujevac Journal of Mathematics, Tome 47 (2023) no. 2, p. 173 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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Let $G$ be a graph of order $n$ with adjacency matrix $A(G)$. The eigenvalues of matrix $ S(G)=J_n-I_n-2A(G)$, where $J_n$ is the $n$ by $n$ matrix with all entries $1$, are called the Seidel eigenvalues of $G$. Let $\mathcal{G}(n,r)$ be the set of all graphs of order $n$ with a single Seidel eigenvalue with multiplicity $r$. In the present work, we will characterize all graphs in the class $\mathcal{G}(n,n-i)$ for $i=1,2$ and for the case $i=3$ our characterization is done by this condition that the nullity of $S(G)$ is zero. If the nullity of $S(G)$ is not zero the problem is solved in special cases.
Classification : 05C50, 05C35
Keywords: interlacing theorem, Seidel eigenvalue, Seidel switching, nullity 
@article{KJM_2023_47_2_a0,
     author = {Modjtaba Ghorbani and Mardjan Hakimi-Nezhaad and Bo Zhou},
     title = {Graphs with at most {Four} {Seidel} {Eigenvalues}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {173 },
     year = {2023},
     volume = {47},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2023_47_2_a0/}
}
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Modjtaba Ghorbani; Mardjan Hakimi-Nezhaad; Bo Zhou. Graphs with at most Four Seidel Eigenvalues. Kragujevac Journal of Mathematics, Tome 47 (2023) no. 2, p. 173 . http://geodesic.mathdoc.fr/item/KJM_2023_47_2_a0/