Automorphisms of trivalent graphs
نویسندگان
چکیده
Let Gg,b be the set of all uni/trivalent graphs representing the combinatorial structures of pant decompositions of the oriented surface ⌃g,b of genus g with b boundary components. We describe the set Ag,b of all automorphisms of graphs in Gg,b showing that, up to suitable moves changing the graph within Gg,b, any such automorphism can be reduced to elementary switches of adjacent edges.
منابع مشابه
An Infinite Family of 4-arc-transitive Cubic Graphs Each with Girth 12
If p is any prime, and 6 is that automorphism of the group SL(3,/>) which takes each matrix to the transpose of its inverse, then there exists a connected trivalent graph F(p) on ^p(p—\)(p — \) vertices with the split extension SL(3,/?)<0> as a group of automorphisms acting regularly on its 4-arcs. In fact if/? / 3 then this group is the full automorphism group of f(p), while the graph F(3) is ...
متن کاملThe Volume Conjecture for Augmented Knotted Trivalent Graphs
We propose to generalize the volume conjecture to knotted trivalent graphs and we prove the conjecture for all augmented knotted trivalent graphs. As a corollary we find that for any link L there is a link containing L for which the volume conjecture holds.
متن کاملClassification of trivalent symmetric graphs of small order
CLASSIFICATION OF TRIVALENT SYMMETRIC GRAPHS OF SMALL ORDER Marston Conder and Margaret Morton Department of Mathematics University of Auckland Private Bag 92019 Auckland NEW ZEALAND A classification is given of all finite connected trivalent symmetric graphs on up to 240 vertices, based on an analysis of short relators in their automorphism groups. SUBJECT CLASSIFICATION 05C25(Primary) 20F05(S...
متن کاملVertex-transitive Haar graphs that are not Cayley graphs
In a recent paper (arXiv:1505.01475 ) Estélyi and Pisanski raised a question whether there exist vertex-transitive Haar graphs that are not Cayley graphs. In this note we construct an infinite family of trivalent Haar graphs that are vertex-transitive but non-Cayley. The smallest example has 40 vertices and is the well-known Kronecker cover over the dodecahedron graph G(10, 2), occurring as the...
متن کاملA trivalent graph of girth 17
A family of trivalent graphs is described that includes most of the known trivalent cages. A new graph in this family is the smallest trivalent graph of girth 17 yet discovered.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Eur. J. Comb.
دوره 34 شماره
صفحات -
تاریخ انتشار 2013