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The path graph P_n is a tree with two nodes of vertex degree 1, and the other n-2 nodes of vertex degree 2. A path graph is therefore a graph that can be drawn so that all of ...

A perspective collineation with center O and axis o not incident is called a geometric homology. A geometric homology is said to be harmonic if the points A and A^' on a line ...

A function which satisfies f(tx,ty)=t^nf(x,y) for a fixed n. Means, the Weierstrass elliptic function, and triangle center functions are homogeneous functions. A ...

The triangle center with triangle center function alpha=A.

Dijkstra's algorithm is an algorithm for finding a graph geodesic, i.e., the shortest path between two graph vertices in a graph. It functions by constructing a shortest-path ...

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 common incircle of the medial triangle DeltaM_AM_BM_C (left figure) and the congruent triangle DeltaQ_AQ_BQ_C, where Q_i are the midpoints of the line segment joining the ...

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; ...