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The word "rigid" has two different meaning when applied to a graph. Firstly, a rigid graph may refer to a graph having a graph automorphism group containing a single element. ...

The cocktail party graph of order n, also called the hyperoctahedral graph (Biggs 1993, p. 17), n-octahedron graph O_n (Jungerman and Ringel 1978), matching graph (Arvind et ...

The n-crown graph for an integer n>=3 is the graph with vertex set {x_0,x_1,...,x_(n-1),y_0,y_1,...,y_(n-1)} (1) and edge set {(x_i,y_j):0<=i,j<=n-1,i!=j}. (2) It is ...

In graph theory, a cycle graph C_n, sometimes simply known as an n-cycle (Pemmaraju and Skiena 2003, p. 248), is a graph on n nodes containing a single cycle through all ...

The ditrigonal icosidodecahedral graph is the skeleton of the cube 5-compound, ditrigonal dodecadodecahedron, great ditrigonalIcosidodecahedron, and small ditrigonal ...

The dodecadodecahedral graph is the skeleton of the dodecadodecahedron, great dodecahemicosahedron, and small dodecahemicosahedron. It is illustrated above in several ...

The odd graph O_n of order n is a graph having vertices given by the (n-1)-subsets of {1,...,2n-1} such that two vertices are connected by an edge iff the associated subsets ...

Let N steps of equal length be taken along a line. Let p be the probability of taking a step to the right, q the probability of taking a step to the left, n_1 the number of ...

The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any ...

The word polytope is used to mean a number of related, but slightly different mathematical objects. A convex polytope may be defined as the convex hull of a finite set of ...