Geodesic
On a~class of coedge regular graphs
Izvestiya. Mathematics , Tome 69 (2005) no. 6, pp. 1169-1187

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We study graphs in which $\lambda(a,b)=\lambda_1,\lambda_2$ for every edge $\{a,b\}$ and all $\mu$-subgraphs are 2-cocliques. We give a description of connected edge-regular graphs for $k\geqslant(b_1^2+3b_1-4)/2$. In particular, the following examples confirm that the inequality $k>b_1(b_1+3)/2$ is a sharp bound for strong regularity: the $n$-gon, the icosahedron graph, the graph in $\operatorname{MP}(6)$ and the distance-regular graph of diameter 4 with intersection massive $\{x,x-1,4,1;1,2,x-1,x\}$, which is an antipodal 3-covering of the strongly regular graph with parameters $((x+2)(x+3)/6,x,0,6)$. 
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     author = {A. A. Makhnev and D. V. Paduchikh},
     title = {On a~class of coedge regular graphs},
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     number = {6},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2005_69_6_a4/}
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A. A. Makhnev; D. V. Paduchikh. On a~class of coedge regular graphs. Izvestiya. Mathematics , Tome 69 (2005) no. 6, pp. 1169-1187. http://geodesic.mathdoc.fr/item/IM2_2005_69_6_a4/