WebAbstract. Using an analysis of the clique structure and only the most elementary group theory, we determine the automorphism group of the Johnson graph J ( n, i), for n ≠ 2 i. … Web1 de nov. de 2024 · Then X is a Johnson graph or is doubly covered by a Johnson graph. More precisely, in the latter case X is the quotient of the Johnson graph J (2 d, d) by an automorphism of the form τω, where τ is the automorphism sending each d-set to its complement, and ω is an element of order at most 2 in Aut (X) with at least 8 fixed …
Quaternion group – Wikipedia – Enzyklopädie
Web1 de jan. de 1973 · We are now able to list the automorphism groups for several common families of graphs. 20 The Automorphism Group of a Graph Chapt. 3 3-4. Thm. 3-18. Graphs with a Given Automorphism Group Every finite group is the automorphism group of some graph. For a proof of this theorem, due to Frucht [ F 4 ] , see Section 4-2. … Web1 de abr. de 2005 · The merged Johnson graph J (n, m)I is the union of the distance i graphs J (n, m)i of the Johnson graph J (n, m) for i ∈ I, where Ø ≠ I ⊆ {1,..., m } and 2 ≤ … inc p2
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Web4 de jan. de 2016 · It isn't the Johnson graphs themselves that were a scourge to theorists. It's more that the Johnson graphs showed that certain difficult structural properties (mentioned above) are possible and nobody knew a general method for handling these properties. Once Babai showed that only the Johnson graphs caused that structure, the … Webgroup of permutations is generated by (xi,xj), (yk,yℓ), and (x,y) Qn i=1(xi,yi). Thus, the automorphism group is isomorphic to S2 n ⋉Z2. The Petersen Graph is one of the most important graphs. In fact, en-tire books have been written about the Petersen graph [16]. The Petersen graph K(5,2) is the graph where the vertex set is all 2-element ... Web23 de dez. de 2024 · Babai conjectured that Hamming and Johnson graphs are the only primitive distance-regular graphs of diameter whose automorphism group has sublinear minimal degree. We confirm this conjecture for non-geometric primitive distance-regular graphs of bounded diameter. inc or incorporated