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The sum I over all internal (circular) nodes of the paths from the root of an extended binary tree to each node. For example, in the tree above, the internal path length is ...

The all-pairs shortest path problem is the determination of the shortest graph distances between every pair of vertices in a given graph. The problem can be solved using n ...

A graph G on more than two vertices is said to be k-connected (or k-vertex connected, or k-point connected) if there does not exist a vertex cut of size k-1 whose removal ...

The connected domination number of a connected graph G, denoted d(G), is the size of a minimum connected dominating set of a graph G. The maximum leaf number l(G) and ...

A set which is connected but not simply connected is called multiply connected. A space is n-multiply connected if it is (n-1)-connected and if every map from the n-sphere ...

A topological space is locally connected at the point x if every neighborhood of x contains a connected open neighborhood. It is called locally connected if it is locally ...

A pathwise-connected domain is said to be simply connected (also called 1-connected) if any simple closed curve can be shrunk to a point continuously in the set. If the ...

A connected set is a set that cannot be partitioned into two nonempty subsets which are open in the relative topology induced on the set. Equivalently, it is a set which ...

A graph is said to be H^*-connected if it is either Hamilton-connected or Hamilton-laceable. S. Wagon (pers. comm., May. 20, 2013; Dupuis and Wagon 2014) conjecture that all ...

The connected sum M_1#M_2 of n-manifolds M_1 and M_2 is formed by deleting the interiors of n-balls B_i^n in M_i^n and attaching the resulting punctured manifolds M_i-B^._i ...