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A graph G is said to be disconnected if it is not connected, i.e., if there exist two nodes in G such that no path in G has those nodes as endpoints. The numbers of ...

The distance d(u,v) between two vertices u and v of a finite graph is the minimum length of the paths connecting them (i.e., the length of a graph geodesic). If no such path ...

The Pell graph Pi_n is the graph defined as follows. Consider n-tuples of (0,1,2) such that maximal blocks of an odd number of 2's are forbidden. Take these as the vertices ...

The fundamental group of an arcwise-connected set X is the group formed by the sets of equivalence classes of the set of all loops, i.e., paths with initial and final points ...

The line integral of a vector field F(x) on a curve sigma is defined by int_(sigma)F·ds=int_a^bF(sigma(t))·sigma^'(t)dt, (1) where a·b denotes a dot product. In Cartesian ...

In discrete percolation theory, site percolation is a percolation model on a regular point lattice L=L^d in d-dimensional Euclidean space which considers the lattice vertices ...

Deck transformations, also called covering transformations, are defined for any cover p:A->X. They act on A by homeomorphisms which preserve the projection p. Deck ...

A connected bipartite graph is called Hamilton-laceable, a term apparently introduced in Simmons (1978), if it has a u-v Hamiltonian path for all pairs of vertices u and v, ...

A flow line for a map on a vector field F is a path sigma(t) such that sigma^'(t)=F(sigma(t)).

A maximally nonhamiltonian graph is a nonhamiltonian graph G for which G+e is Hamiltonian for each edge e in the graph complement of G^_, i.e., every two nonadjacent vertices ...