Geodesic
Seidel Energy of Iterated Line Graphs of Regular Graphs
Kragujevac Journal of Mathematics, Tome 39 (2015) no. 1, p. 7 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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The Seidel matrix $S(G)$ of a graph $G$ is the square matrix whose $(i,j)$-entry is equal to $-1$ or $1$ if the $i$-th and $j$-th vertices of $G$ are adjacent or non-adjacent, respectively, and is zero if $i=j$. The Seidel energy of $G$ is the sum of the absolute values of the eigenvalues of $S(G)$. We show that if $G$ is regular of order $n$ and of degree $r\geq3$, then for each $k\geq2$, the Seidel energy of the $k$-th iterated line graph of $G$ depends solely on $n$ and $r$. This result enables the construction of pairs of non-cospectral, Seidel equienergetic graphs of the same order.
Classification : 05C50, 05C07
Keywords: Seidel spectrum, Seidel energy, line graph, regular graph 
@article{KJM_2015_39_1_a0,
     author = {Harishchandra S. Ramane and Ivan Gutman and Mahadevappa M. Gundloor},
     title = {Seidel {Energy} of {Iterated} {Line} {Graphs} of {Regular} {Graphs}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {7 },
     year = {2015},
     volume = {39},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2015_39_1_a0/}
}
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Harishchandra S. Ramane; Ivan Gutman; Mahadevappa M. Gundloor. Seidel Energy of Iterated Line Graphs of Regular Graphs. Kragujevac Journal of Mathematics, Tome 39 (2015) no. 1, p. 7 . http://geodesic.mathdoc.fr/item/KJM_2015_39_1_a0/