Distance-regular graphs with intersectuion arrays $\{42,30,12;1,6,28\}$ and $\{60,45,8;1,12,50\}$ do not exist

I. N. Belousov; A. A. Makhnev

Geodesic

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Distance-regular graphs with intersectuion arrays $\{42,30,12;1,6,28\}$ and $\{60,45,8;1,12,50\}$ do not exist

I. N. Belousov ; A. A. Makhnev

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1506-1512

Voir la notice de l'article provenant de la source Math-Net.Ru

Résumé

Koolen and Park obtained the list of intersection arrays for Shilla graphs with $b=3$. In particular distance-regular graph with intersectuion array $\{42,30,12;1,6,28\}$ is Shilla graphs with $b=3$. Gavrilyuk and Makhnev investigated properties of a graph with intersectuion array $\{60,45,8;1,12,50\}$. We proved that distance-regular graphs with intersectuion arrays $\{42, 30,12;1,6,28\}$ and $\{60,45,8;1,12,50\}$ do not exist.

Keywords: distance-regular graph, Shilla graph, triple intersection numbers.

@article{SEMR_2018_15_a81,
     author = {I. N. Belousov and A. A. Makhnev},
     title = {Distance-regular graphs with intersectuion arrays $\{42,30,12;1,6,28\}$ and $\{60,45,8;1,12,50\}$ do not exist},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1506--1512},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a81/}
}

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I. N. Belousov; A. A. Makhnev. Distance-regular graphs with intersectuion arrays $\{42,30,12;1,6,28\}$ and $\{60,45,8;1,12,50\}$ do not exist. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1506-1512. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a81/