Jan 20, 2025 · "The" octahedral graph is the 6-node 12-edge Platonic graph having the connectivity of the octahedron. It is isomorphic to the circulant graph Ci_6(1,2), the cocktail party graph K_(3×2), the complete tripartite graph K_(2,2,2), and the 4-dipyramidal graph.

The octahedron is a symmetric graph. If we can find 4 independent paths between a vertex and one of its neighbors, and again between a vertex and the one other vertex which is not its neighbor, then the graph is 4-connected.

Jun 3, 2013 · In this paper, we will present the concepts of planar graphs, Euler’s characteristic formula, and Platonic solids and show their relationships to one another. After first defining planar graphs, we will prove that Euler’s characteristic holds true for any of them.

The octahedron is one of 5 Platonic graphs. These solids have congruent vertices, faces, edges and angles. In the planar draing and the graph you can clearly see that a octahedron has got 6 vertices, 12 edges and 8 faces. This follows Euler's formula.

Mar 1, 2011 · In this paper, we prove sharp results about the case L = {O 6}, where O 6 is the graph with 6 vertices and 12 edges, given by the edges of an octahedron. Among others, we prove the following results.

Jan 29, 2019 · A magic labeling of a graph G G with q q edges is an edge labeling by the numbers 1, 2, 3, …, q 1, 2, 3, …, q so that the sum of the labels of all the edges incident with any vertex is the same. We need to find a magic labeling of the octahedron graph.

Here is a planar drawing of the octahedron graph, with a 3-coloring of the vertices. (Vertices of color 1 are indicated by a 1.) Proposition 0.2 (Exercise 1b). Let G be the edge graph of the octahedron. Then (G) = 3. Proof. As an example of a proper 3-coloring, see the picture above. By this example, (G) 3. We just need to show that (3) 3.

There are exactly 8 strictly convex deltahedra: the tetrahedron, octahedron, icosahedron, triangular bipyramid, pentagonal bipyramid, gyroelongated square bipyramid, triaugmented triangular prism, and snub disphenoid.

In this lecture we shall start with describing some major areas in the classical extremal graph theory. Then we shall concentrate on some open conjectures, problems. What is an extremal graph problem? We fix some objects, they form the Universe.

We prove that all 3-connected 4-regular planar graphs can be generated from the Octahedron Graph, using three operations. We generated these graphs up to 15 vertices inclusive.