Distinguishing Cartesian powers of graphs.
Distinguishing Cartesian Products of Countable Graphs
The distinguishing number D(G) of a graph G is the minimum number of colors needed to color the vertices of G such that the coloring is preserved only by the trivial automorphism. In this paper we improve results about the distinguishing number of Cartesian products of finite and infinite graphs by removing restrictions to prime or relatively prime factors.
Distinguishing chromatic numbers of bipartite graphs.
Distinguishing infinite graphs.
Distinguishing numbers for graphs and groups.
Double coverings and reflexive abelian hypermaps.
Doubly Primitive Vertex Stabilisers in Graphs.
Dynamic cage survey.
Edge-Transitive Lexicographic and Cartesian Products
In this note connected, edge-transitive lexicographic and Cartesian products are characterized. For the lexicographic product G ◦ H of a connected graph G that is not complete by a graph H, we show that it is edge-transitive if and only if G is edge-transitive and H is edgeless. If the first factor of G ∘ H is non-trivial and complete, then G ∘ H is edge-transitive if and only if H is the lexicographic product of a complete graph by an edgeless graph. This fixes an error of Li, Wang, Xu, and Zhao...
Edge-Transitivity of Cayley Graphs Generated by Transpositions
Let S be a set of transpositions generating the symmetric group Sn (n ≥ 5). The transposition graph of S is defined to be the graph with vertex set {1, . . . , n}, and with vertices i and j being adjacent in T(S) whenever (i, j) ∈ S. In the present note, it is proved that two transposition graphs are isomorphic if and only if the corresponding two Cayley graphs are isomorphic. It is also proved that the transposition graph T(S) is edge-transitive if and only if the Cayley graph Cay(Sn, S) is edge-transitive....
Either tournaments or algebras? (Preliminary communication)
Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups.
End-faithful spanning trees of countable graphs with prescribed sets of rays
We prove that a countable connected graph has an end-faithful spanning tree that contains a prescribed set of rays whenever this set is countable, and we show that this solution is, in a certain sense, the best possible. This improves a result of Hahn and Širáň Theorem 1.
Endomorphisms of symbolic algebraic varieties
The theorem of Ax says that any regular selfmapping of a complex algebraic variety is either surjective or non-injective; this property is called surjunctivity and investigated in the present paper in the category of proregular mappings of proalgebraic spaces. We show that such maps are surjunctive if they commute with sufficiently large automorphism groups. Of particular interest is the case of proalgebraic varieties over infinite graphs. The paper intends to bring out relations between model theory,...
End-regular and End-orthodox generalized lexicographic products of bipartite graphs
A graph X is said to be End-regular (End-orthodox) if its endomorphism monoid End(X) is a regular (orthodox) semigroup. In this paper, we determine the End-regular and the End-orthodox generalized lexicographic products of bipartite graphs.
Enumeration of hamiltonian paths in Caley diagrams.
Equivalence of the strengthened Hanna Neumann conjecture and the amalgamated graph conjecture.
Erratum to : “Green kernel estimates and the full Martin boundary for random walks on lamplighter groups and Diestel–Leader graphs”
Etude du spectre pour certains noyaux sur un arbre
Expansion and random walks in : I
We prove that the Cayley graphs of are expanders with respect to the projection of any fixed elements in generating a Zariski dense subgroup.