4,021 research outputs found
Strongly regular edge-transitive graphs
In this paper, we examine the structure of vertex- and edge-transitive
strongly regular graphs, using normal quotient reduction. We show that the
irreducible graphs in this family have quasiprimitive automorphism groups, and
prove (using the Classification of Finite Simple Groups) that no graph in this
family has a holomorphic simple automorphism group. We also find some
constraints on the parameters of the graphs in this family that reduce to
complete graphs.Comment: 23 page
Automorphism groups of countable algebraically closed graphs and endomorphisms of the random graph
We establish links between countable algebraically closed graphs and the
endomorphisms of the countable universal graph . As a consequence we show
that, for any countable graph , there are uncountably many maximal
subgroups of the endomorphism monoid of isomorphic to the automorphism
group of . Further structural information about End is established
including that Aut arises in uncountably many ways as a
Sch\"{u}tzenberger group. Similar results are proved for the countable
universal directed graph and the countable universal bipartite graph.Comment: Minor revision following referee's comments. 27 pages, 3 figure
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