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A spanning tree of a graph on n vertices is a subset of n-1 edges that form a tree (Skiena 1990, p. 227). For example, the spanning trees of the cycle graph C_4, diamond ...

Let s_k be the number of independent vertex sets of cardinality k in a graph G. The polynomial I(x)=sum_(k=0)^(alpha(G))s_kx^k, (1) where alpha(G) is the independence number, ...

A k-matching in a graph G is a set of k edges, no two of which have a vertex in common (i.e., an independent edge set of size k). Let Phi_k be the number of k-matchings in ...

A topological space decomposes into its connected components. The connectedness relation between two pairs of points satisfies transitivity, i.e., if a∼b and b∼c then a∼c. ...

The maximum leaf number l(G) of a graph G is the largest number of tree leaves in any of its spanning trees. (The corresponding smallest number of leaves is known as the ...

The mathematical study of the properties of the formal mathematical structures called graphs.

A Hamiltonian cycle, also called a Hamiltonian circuit, Hamilton cycle, or Hamilton circuit, is a graph cycle (i.e., closed loop) through a graph that visits each node ...

The multiplicity of a multigraph is its maximum edge multiplicity.

A graceful labeling (or graceful numbering) is a special graph labeling of a graph on m edges in which the nodes are labeled with a subset of distinct nonnegative integers ...

A labeling phi of (the vertices) of a graph G with positive integers taken from the set {1,2,...,r} is said to be r-distinguishing if no graph automorphism of G preserves all ...