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"The" I graph is the path graph on two vertices: P_2. An I-graph I(n,j,k) for 1<=j,k<n and j,k!=n/2 is a generalization of a generalized Petersen graph and has vertex set ...

The Icosian game, also called the Hamiltonian game (Ball and Coxeter 1987, p. 262), is the problem of finding a Hamiltonian cycle along the edges of an dodecahedron, i.e., a ...

In the early 1950s, Ernst Straus asked 1. Is every region illuminable from every point in the region? 2. Is every region illuminable from at least one point in the region? ...

A nonhamiltonian graph is a graph that is not Hamiltonian. All disconnected graphs are therefore nonhamiltoinian, as are acylic graphs. Classes of connected graphs that are ...

An extended rooted binary tree satisfying the following conditions: 1. Every node has two children, each colored either red or black. 2. Every tree leaf node is colored ...

A self-complementary graph is a graph which is isomorphic to its graph complement. The numbers of simple self-complementary graphs on n=1, 2, ... nodes are 1, 0, 0, 1, 2, 0, ...

The tractrix arises in the following problem posed to Leibniz: What is the path of an object starting off with a vertical offset when it is dragged along by a string of ...

Vassiliev invariants, discovered around 1989, provided a radically new way of looking at knots. The notion of finite type (a.k.a. Vassiliev) knot invariants was independently ...

The m-book graph is defined as the graph Cartesian product B_m=S_(m+1) square P_2, where S_m is a star graph and P_2 is the path graph on two nodes. The generalization of the ...

A helix, sometimes also called a coil, is a curve for which the tangent makes a constant angle with a fixed line. The shortest path between two points on a cylinder (one not ...