Geodesic
Strictly Deza line graphs
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 1, pp. 165-177

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For a given graph $G$, its line graph $L(G)$ is a graph such that its vertices represent the edges of $G$ and two vertices are adjacent if and only if the corresponding edges of $G$ have exactly one common vertex. A $k$-regular graph of diameter 2 with $v$ vertices is called a strictly Deza graph with parameters $(v,k,b,a)$ if it is not strongly regular and any two vertices have either $a$ or $b$ common neighbors. We present a classification of strictly Deza graphs that are line graphs.
Keywords: line graphs, strictly Deza graphs. 
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     title = {Strictly {Deza} line graphs},
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V. V. Kabanov; A. V. Mityanina. Strictly Deza line graphs. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 1, pp. 165-177. http://geodesic.mathdoc.fr/item/TIMM_2012_18_1_a12/