On distance regular graphs with diameter 3 and degree 44
Abstract
Distance-regular graph Γ with strongly regular graphs Γ2 and Γ3 has intersection array {r(c2 +1)+a3, rc2, a3 +1; 1, c2, r(c2 +1)} (M. S. Nirova). For distance-regular graph with diameter 3 and degree 44 there are 7 fisiable intersection arrays. For each of them the graph Γ3 is strongly regular. For intersection array {44,30,5;1,3,40} we have a3 = 4, c2 = 3 and r = 10, Γ2 has parameters (540, 440, 358, 360) and Γ3 has parameters (540, 55, 10, 5). This graph does not exist (Koolen-Park). For intersection array {44, 35, 3; 1, 5, 42} the graph Γ3 has parameters (375, 22, 5, 1). Graph Γ3 does nor exist (local subgraph is the union of isolated 6-cliques). In this paper it is proved that distance-regular graphs with intersection arrays {44, 36, 5; 1, 9, 40}, {44, 36, 12; 1, 3, 33} and {44, 42, 5; 1, 7, 40} do not exist.
Supporting agencies: The research was carried out with the support of the Natural Science Foundation of China (project No. 12171126) and a grant from the Laboratory of Engineering Modeling and Statistical Computing of Hainan Province
About the Authors
M. Chen
Universitet provintsii Khaynan
China
China
Kheykou
A. A. Makhnev
Ural Federal University
Russian Federation
Russian Federation
N. N. Krasovsky Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences
Yekaterinburg
V. S. Klimin
Ural Federal University
Russian Federation
Russian Federation
Yekaterinburg
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Review
For citations:
Chen M., Makhnev A.A., Klimin V.S. On distance regular graphs with diameter 3 and degree 44. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2024;32(1):57-63. (In Russ.)
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