AbstractFor n = 2k − 1 we prove, via a counting argument, that for any tree J with vertex set T, if J is isometrically embedded in the n-cube Qn, then there exists a subgroup G of Aut(Qn) such that {g(T)¦g∈G} is a vertex partition of Qn. This generalizes the theorem of Hamming on the existence of perfect single-error-correcting codes, which corresponds to the case where J is an n-star. For the special case of an antipodal path we give an explicit construction of the group G
AbstractAn isometric path is merely any shortest path between two vertices. If the vertices of the h...
Let n be a positive integer, let ∏n denote the lattice of partitions of {1, 2, ..., n} and let Sn de...
AbstractLet k, ℓ be positive integers. Let G be a graph of order kℓ. It is shown that if G is a comp...
AbstractFor n = 2k − 1 we prove, via a counting argument, that for any tree J with vertex set T, if ...
AbstractAn isometric path is merely any shortest path between two vertices. If the vertices of the h...
AbstractIn this note, we give a counter-example for a lemma of Harary and Lewinter about partitionin...
Tree-like isometric subgraphs of hypercubes, or tree-like partial cubes as we shall call them, are a...
A distinguishing partition of a set X with automorphism group aut(X) is a partition of X that is fix...
Tree-like isometric subgraphs of hypercubes, or tree-like partial cubes as we shall call them, are a...
We define the concept of regular partition of a graph Γ and its relationship to the automorphism gro...
Let H be an induced subgraph of the torus Ckm. We show that when k≥3 is even and |V(H)| divid...
A distinguishing partition for an action of a group Γ on a set X is a partition of X that is preserv...
AbstractThe k-wheel Wk is the graph obtained as a join of a vertex and the cycle of length k. It is ...
Abstract. We explore the well-known Stanley conjecture stat-ing that the symmetric chromatic polynom...
Let τ(G) denote the number of vertices in a longest path of the graph G and let k₁ and k₂ be positiv...
AbstractAn isometric path is merely any shortest path between two vertices. If the vertices of the h...
Let n be a positive integer, let ∏n denote the lattice of partitions of {1, 2, ..., n} and let Sn de...
AbstractLet k, ℓ be positive integers. Let G be a graph of order kℓ. It is shown that if G is a comp...
AbstractFor n = 2k − 1 we prove, via a counting argument, that for any tree J with vertex set T, if ...
AbstractAn isometric path is merely any shortest path between two vertices. If the vertices of the h...
AbstractIn this note, we give a counter-example for a lemma of Harary and Lewinter about partitionin...
Tree-like isometric subgraphs of hypercubes, or tree-like partial cubes as we shall call them, are a...
A distinguishing partition of a set X with automorphism group aut(X) is a partition of X that is fix...
Tree-like isometric subgraphs of hypercubes, or tree-like partial cubes as we shall call them, are a...
We define the concept of regular partition of a graph Γ and its relationship to the automorphism gro...
Let H be an induced subgraph of the torus Ckm. We show that when k≥3 is even and |V(H)| divid...
A distinguishing partition for an action of a group Γ on a set X is a partition of X that is preserv...
AbstractThe k-wheel Wk is the graph obtained as a join of a vertex and the cycle of length k. It is ...
Abstract. We explore the well-known Stanley conjecture stat-ing that the symmetric chromatic polynom...
Let τ(G) denote the number of vertices in a longest path of the graph G and let k₁ and k₂ be positiv...
AbstractAn isometric path is merely any shortest path between two vertices. If the vertices of the h...
Let n be a positive integer, let ∏n denote the lattice of partitions of {1, 2, ..., n} and let Sn de...
AbstractLet k, ℓ be positive integers. Let G be a graph of order kℓ. It is shown that if G is a comp...
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