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This article is cited in 6 scientific papers (total in 6 papers)
Discrete mathematics and mathematical cybernetics
On distance-regular graph $\Gamma$ with strongly regular graphs $\Gamma_2$ and $\Gamma_3$
M. S. Nirova Kabardino-Balkarian State University named after H.M. Berbekov,
st. Chernyshevsky, 175,
360004, Nalchik, Russia
Abstract:
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 $\Gamma_3$.
Received December 20, 2017, published March 1, 2018
Citation:
M. S. Nirova, “On distance-regular graph $\Gamma$ with strongly regular graphs $\Gamma_2$ and $\Gamma_3$”, Sib. Èlektron. Mat. Izv., 15 (2018), 175–185
Linking options:
https://www.mathnet.ru/eng/semr908 https://www.mathnet.ru/eng/semr/v15/p175
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