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The detour matrix Delta, sometimes also called the maximum path matrix or maximal topological distances matrix, of a graph is a symmetric matrix whose (i,j)th entry is the ...

Ore (1962) noted that not only does a tree possesses a unique shortest path between any two vertices, but that there also exist also other connected graphs having the same ...

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 ...

A puzzle involving disentangling a set of rings from a looped double rod, originally used by French peasants to lock chests (Steinhaus 1999). The word "baguenaudier" means ...

The complete bipartite graph K_(1,3) is a tree known as the "claw." It is isomorphic to the star graph S_4, and is sometimes known as the Y graph (Horton and Bouwer 1991; ...

Given any tree T having v vertices of vertex degrees of 1 and 3 only, form an n-expansion by taking n disjoint copies of T and joining corresponding leaves by an n-cycle ...

The orchard-planting problem (also known as the orchard problem or tree-planting problem) asks that n trees be planted so that there will be r(n,k) straight rows with k trees ...

If K is a simplicial complex, let V be the vertex set of K. Furthermore, let K be the collection of all subsets {a_0,...,a_n} of V such that the vertices a_0, ..., a_n span a ...

The Balaban 11-cage is the unique 11-cage graph, derived via a tree excision from the 12-cage graph by Balaban (1973) and proven unique by McKay and Myrvold in 2003. It is ...

The taxicab metric, also called the Manhattan distance, is the metric of the Euclidean plane defined by g((x_1,y_1),(x_2,y_2))=|x_1-x_2|+|y_1-y_2|, for all points ...