Geodesic
The structure of trivalent graphs with minimal eigenvalue gap
Journal of Algebraic Combinatorics, Tome 6 (1997) no. 4, pp. 321-329.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $G$ be a connected trivalent graph on $n$vertices ( $nge$10) such that among all connected trivalentgraphs on $n$ vertices, $G$ has the largest possiblesecond eigenvalue. We show that $G$ must be reduced path-like, i.e. $G$ must be of the form: where theends are one of the following:(the right-hand end block is the mirror image of one of the blocks shown)and the middle blocks are one of the following: This partially solves a conjecture implicit in a paper of Bussemaker, $Ccaron$obelji $cacute$, Cvetkovi $cacute$, and Seidel [3].
Keywords: trivalent graph, eigenvalue 
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     author = {Guiduli, Barry},
     title = {The structure of trivalent graphs with minimal eigenvalue gap},
     journal = {Journal of Algebraic Combinatorics},
     pages = {321--329},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_1997__6_4_a3/}
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Guiduli, Barry. The structure of trivalent graphs with minimal eigenvalue gap. Journal of Algebraic Combinatorics, Tome 6 (1997) no. 4, pp. 321-329. http://geodesic.mathdoc.fr/item/JAC_1997__6_4_a3/