Edge-reconstruction of minimally 3-connected planar graphs.
Eigenvalue Conditions for Induced Subgraphs
Necessary conditions for an undirected graph G to contain a graph H as induced subgraph involving the smallest ordinary or the largest normalized Laplacian eigenvalue of G are presented.
Eigenvectors and reconstruction.
Embedding a forest in a graph.
Embeddings of hamiltonian paths in faulty k-ary 2-cubes
It is well known that the k-ary n-cube has been one of the most efficient interconnection networks for distributed-memory parallel systems. A k-ary n-cube is bipartite if and only if k is even. Let (X,Y) be a bipartition of a k-ary 2-cube (even integer k ≥ 4). In this paper, we prove that for any two healthy vertices u ∈ X, v ∈ Y, there exists a hamiltonian path from u to v in the faulty k-ary 2-cube with one faulty vertex in each part.
Equivalences between isomorphism classes on infinite graphs
The paper studies some equivalence relations between isomorphism classes of countable graphs which correspond in a certain sense to various distances between isomorphism classes of finite graphs.