Loading...
Please wait, while we are loading the content...
Similar Documents
On Locally Projective Graphs of Girth 5
| Content Provider | Semantic Scholar |
|---|---|
| Author | Ivanov, Alexander A. Ivanov, Andrei |
| Copyright Year | 1998 |
| Abstract | Let0 be a graph and G be a 2-arc transitive automorphism group of 0. For a vertexx ∈ 0 let G(x)0(x) denote the permutation group induced by the stabilizer G(x) of x in G on the set0(x) of vertices adjacent to x in 0. Then0 is said to be a locally projective graph of type (n,q) if G(x)0(x) containsPSLn(q) as a normal subgroup in its natural doubly transitive action. Suppose that 0 is a locally projective graph of type (n,q), for somen ≥ 3, whose girth (that is, the length of a shortest cycle) is 5 and suppose that G(x) acts faithfully on0(x). (The case of unfaithful action was completely settled earlier.) We show that under these conditions either n = 4, q = 2,0 has 506 vertices and G ∼= M23, or q = 4, PSLn(4) ≤ G(x) ≤ PGLn(4), and0 contains the Wells graph on 32 vertices as a subgraph. In the latter case if, for a given n, at least one graph satisfying the conditions exists then there is a universal graph W(n) of which all other graphs for this n are quotients. The graph W(3) satisfies the conditions and has 2 20 vertices. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.maths.tcd.ie/EMIS/journals/JACO/Volume7_3/x9767088u46h714u.fulltext.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Girth (graph theory) Graph - visual representation Graph automorphism Short Subgroup A Nepoviruses Vertex (geometry) |
| Content Type | Text |
| Resource Type | Article |
