Geodesic
Star Complements and Maximal Exceptional Graphs
Publications de l'Institut Mathématique, _N_S_76 (2004) no. 90, p. 25

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If $G$ is a maximal exceptional graph then either (a) $G$ is the cone over a graph switching-equivalent to the line graph $L(K_8)$ or (b) $G$ has $K_8$ as a star complement for the eigenvalue $-2$ (or both). In case (b) it is shown how $G$ can be constructed from $K_8$ using intersecting families of $3$-sets.
DOI : 10.2298/PIM0476025R
Classification : 05C50
Keywords: exceptional graph, eigenvalue, star complement 
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     title = {Star {Complements} and {Maximal} {Exceptional} {Graphs}},
     journal = {Publications de l'Institut Math\'ematique},
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P. Rowlinson. Star Complements and Maximal Exceptional Graphs. Publications de l'Institut Mathématique, _N_S_76 (2004) no. 90, p. 25 . doi: 10.2298/PIM0476025R

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