9 research outputs found
On geometric distance-regular graphs with diameter three
In this paper we study distance-regular graphs with intersection array {(t + 1)s. ts. (t - 1)(s + 1 - psi); 1, 2, (t + 1)psi} (1) where s. t. psi are integers satisfying t >= 2 and 1 = 2, there are only finitely many distance-regular graphs of order (s, t) with mallest eigenvalue -t -1, diameter D = 3 and intersection number c(2) = 2 except for Hamming graphs with diameter three. Moreover, we will show that if a distance-regular graph with intersection array (1) for t = 2 exists then (s, psi) = (15, 9). As Gavrilyuk and Makhnev (2013)[9] proved that the case (s, psi) = (15, 9) does not exist, this enables us to finish the classification of geometric distance-regular graphs with smallest eigenvalue -3, diameter D >= 3 and c(2) >= 2 which was started by the first author (Bang, 2013)[1]. (C) 2013 Elsevier Ltd. All rights reserved.X1121Ysciescopu
Automorphisms of distance regular graph with intersection array 30, 27, 24; 1, 2, 10
Prime divisors of orders of automorphisms and the fixed point subgraphs of automorphisms of prime orders are studied for a hypothetical distance-regular graph with intersection array 30, 27, 24; 1, 2, 10. Let G = Aut(Γ) is nonsolvable group, G = G=S(G) and T is the socle of G. If Γ is vertex-symmetric then (G) is f2g-group, and T ≅= L2(11),M11,U5(2),M22,A11,HiS. © 2019, Sobolev Institute of Mathematics
On automorphisms of a distance-regular graph with intersection array {39, 36, 1; 1, 2, 39}
Possible prime-order automorphisms and their fixed-point subgraphs are found for a hypothetical distance-regular graph with intersection array {39, 36, 1; 1, 2, 39}. It is shownthat graphs with intersection arrays {15, 12, 1; 1, 2, 15}, {35, 32, 1; 1, 2, 35}, and {39, 36, 1; 1, 2, 39} are not vertex-symmetric. © 2016, Pleiades Publishing, Ltd
On automorphisms of a distance-regular graph with intersection array {99, 84, 1; 1, 12, 99}
We find possible orders and fixed point subgraphs of a hypothetical distance-regular graph with intersection array {99, 84, 1; 1, 12, 99}. We show that, for a vertex-symmetric graph Γ with intersection array {99, 84, 1; 1, 12, 99}, its automorphism group is a {2, 3, 5}-group. © 2017, Pleiades Publishing, Ltd
Non-geometric distance-regular graphs of diameter at least with smallest eigenvalue at least
In this paper, we classify non-geometric distance-regular graphs of diameter
at least with smallest eigenvalue at least . This is progress towards
what is hoped to be an eventual complete classification of distance-regular
graphs with smallest eigenvalue at least , analogous to existing
classification results available in the case that the smallest eigenvalue is at
least
Families of Association Schemes on Triples from Two-Transitive Groups
Association schemes on triples (ASTs) are ternary analogues of classical
association schemes. Analogous to Schurian association schemes, ASTs arise from
the actions of two-transitive groups. In this paper, we obtain the sizes and
third valencies of the ASTs obtained from the two-transitive permutation groups
by determining the orbits of the groups' two-point stabilizers. Specifically,
we obtain these parameters for the ASTs obtained from the actions of and
, , , and , and
, some subgroups of , some subgroups of , and the sporadic two-transitive groups. Further, we obtain the
intersection numbers for the ASTs obtained from these subgroups of and , and the sporadic two-transitive groups. In
particular, the ASTs from these projective and sporadic groups are commutative.Comment: 20 pages, 5 table
Distance-regular graphs
This is a survey of distance-regular graphs. We present an introduction to
distance-regular graphs for the reader who is unfamiliar with the subject, and
then give an overview of some developments in the area of distance-regular
graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A.,
Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page