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Vince and Bóna (2012) define an assembly tree T for a connected simple graph G on n nodes as a binary rooted tree with n leavesTree Leaf and n-1 internal nodes and satisfying ...

A maximum irredundant set is an irredundant set of largest possible size in a graph. Note that a maximum irredundant set is not equivalent to a maximal irredundant set, which ...

The minimum leaf number ml(G) of a connected graph G is the smallest number of tree leaves in any of its spanning trees. (The corresponding largest number of leaves is known ...

The Catalan numbers on nonnegative integers n are a set of numbers that arise in tree enumeration problems of the type, "In how many ways can a regular n-gon be divided into ...

Consider a broadcast scheme on a connected graph from an originator vertex v in a graph G consisting of a sequence of parallel calls starting from v. In each time step, every ...

There are a number of hypotraceable and hypohamiltonian graphs associated with Carsten Thomassen. These graphs, illustrated above, are implemented in the Wolfram Language as ...

The lower matching number of a graph is the minimum size of a maximal independent edge set. The (upper) matching number may be similarly defined as the largest size of an ...

A tree not having the complete bipartite graph K_(1,2) with base at the vertex of degree two as a limb (Lu et al. 1993, Lu 1996).

The maximum flow between vertices v_i and v_j in a graph G is exactly the weight of the smallest set of edges to disconnect G with v_i and v_j in different components (Ford ...

The vector field N_f(z)=-(f(z))/(f^'(z)) arising in the definition of the Newtonian graph of a complex univariate polynomial f (Smale 1985, Shub et al. 1988, Kozen and ...