Geodesic
On distance-regular graphs $\Gamma$ of diameter 3 for which $\Gamma_3$ is a triangle-free graph
Diskretnaya Matematika, Tome 33 (2021) no. 4, pp. 61-67

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There exist well-known distance-regular graphs $\Gamma$ of diameter 3 for which $\Gamma_3$ is a triangle-free graph. An example is given by the Johnson graph $J(8,3)$ with the intersection array $\{15,8,3;1,4,9\}$. The paper is concerned with the problem of the existence of distance-regular graphs $\Gamma$ with the intersection arrays $\{78,50,9;1,15,60\}$ and $\{174,110,18;1,30,132\}$ for which $\Gamma_3$ is a triangle-free graph.
Keywords: distance-regular graph, triangle-free graph, triple intersection numbers. 
@article{DM_2021_33_4_a5,
     author = {A. A. Makhnev and Venbin Guo},
     title = {On distance-regular graphs $\Gamma$ of diameter 3 for which $\Gamma_3$ is a triangle-free graph},
     journal = {Diskretnaya Matematika},
     pages = {61--67},
     publisher = {mathdoc},
     volume = {33},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2021_33_4_a5/}
}
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A. A. Makhnev; Venbin Guo. On distance-regular graphs $\Gamma$ of diameter 3 for which $\Gamma_3$ is a triangle-free graph. Diskretnaya Matematika, Tome 33 (2021) no. 4, pp. 61-67. http://geodesic.mathdoc.fr/item/DM_2021_33_4_a5/