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Graph of a triangular bipyramid. According to Steinitz's theorem, a graph can be represented as the skeleton of a polyhedron if it is a planar (the edges of the graph do not cross, but intersect at the point) and three-connected graph (one of any two vertices leaves a connected subgraph
The Fritsch graph is one of only six connected graphs in which the neighborhood of every vertex is a cycle of length four or five. More generally, when every vertex in a graph has a cycle of length at least four as its neighborhood, the triangles of the graph automatically link up to form a topological surface called a Whitney triangulation.
The 40th parallel north is a circle of latitude that is 40 degrees north of the Earth's equatorial plane. It crosses Europe , the Mediterranean Sea , Asia , the Pacific Ocean , North America , and the Atlantic Ocean .
Every acute triangle has three inscribed squares (squares in its interior such that all four of a square's vertices lie on a side of the triangle, so two of them lie on the same side and hence one side of the square coincides with part of a side of the triangle). In a right triangle two of the squares coincide and have a vertex at the triangle ...
The nested triangles graph with two triangles is the graph of the triangular prism, and the nested triangles graph with three triangles is the graph of the triangular bifrustum. More generally, because the nested triangles graphs are planar and 3-vertex-connected , it follows from Steinitz's theorem that they all can be represented as convex ...
A subset of vertices in a graph G is called dissociation if it induces a subgraph with maximum degree 1. distance The distance between any two vertices in a graph is the length of the shortest path having the two vertices as its endpoints. domatic A domatic partition of a graph is a partition of the vertices into dominating sets.
The triangle has 3 vertices, each of which pairs with another triangle's vertex, making up another 3 edges. These edges form 3 parallelograms as other faces. [2] If the prism's edges are perpendicular to the base, the lateral faces are rectangles, and the prism is called a right triangular prism. [3]
The Cartesian product of two locally linear regular graphs is again locally linear and regular, with degree equal to the sum of the degrees of the factors. Therefore, one can take Cartesian products of locally linear graphs of degree two (triangles) to produce regular locally linear graphs of every even degree. [1]