Geodesic
On distance-regular graph $\Gamma$ with strongly regular graphs $\Gamma_2$ and $\Gamma_3$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 175-185

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It is investigated distance-regular graphs $\Gamma$ of diameter 3 with strongly regular graphs $\Gamma_2$ and $\Gamma_3$. If $\Gamma$ is antipodal graph then either $\Gamma$ is Taylor graph without triangles or $\bar \Gamma_2$ is pseudo-geometric graph for $GQ(r-1,c_2+1)$. If $\Gamma$ is primitive graph then $\Gamma$ has intersection array $\{r(c_2+1)+a_3,rc_2,a_3+1;1,c_2,r(c_2+1)\}$. Last result gives intersection arrays in the case when $\Gamma_3$ is strongly regular graph without triangles. If $\mu(\Gamma_3)\le 11$, then $\Gamma$ has intersection array $\{14,10,3;1,5,12\}$, $\{119,100,15;1,20,105\}$ or $\{(r+5)((r+3)^2-3)/6,r(r+3)(r+8)/6,r+6;1,(r+3)(r+8)/6,r(r+5)(r+6)/6\}$, $r=4,6,10,16,19,24,28,40,46,52,58,60,70,79$.
Keywords: distance-regular graph, graph with strongly regular $\Gamma_2$ and $\Gamma_3$. 
@article{SEMR_2018_15_a60,
     author = {M. S. Nirova},
     title = {On distance-regular graph $\Gamma$ with strongly regular graphs  $\Gamma_2$ and $\Gamma_3$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {175--185},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a60/}
}
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M. S. Nirova. On distance-regular graph $\Gamma$ with strongly regular graphs  $\Gamma_2$ and $\Gamma_3$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 175-185. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a60/