Purchase Solution

Find values of p for which the faces of a planar p-regular graph are all triangles.

Not what you're looking for?

Ask Custom Question

The faces of a planar p-regular graph are all triangles (that is each face has degree three). Determine, with proof, the values of p for which this is possible. (Remember a p-regular graph has all vertices of degree p).

Attachments
Purchase this Solution
Solution Summary

Values of p for which the faces of a planar p-regular graph are all triangles are found. The solution is detailed and well presented. The solution received a rating of "5" from the student who posted the question.

Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

View More Free Quizzes
Related BrainMass Solutions

  • Planar graph

    We conclude then that a graph G on n vertices with the most edges will have triangles for all its faces.Then each face has three edges on its boundary, and the number of edge-face pairs with the edge bounding the face will be 3f.

  • Outerplanar Graphs

    150387 Outerplanar Graphs A graph is outerplanar if it can be embedded in the plane so that every vertex lies on the boundary of the exterior region. Prove the following: If G = G(p, q) is outerplanar with p >= 2, then q <= 2p - 3. Proof.

  • Electric field near a charged slab

    Find the magnitude of the electric field at all points in space both inside and outside the slab, in terms of x, the distance measured from the central plane of the slab. What is the field for x = 1.00 cm? What is the field for x = 8.00 cm?

  • Outerplanar and Bipartite Graphs

    If there are p and q graph vertices in the two sets, the complete bipartite graph (sometimes also called a complete bigraph) is denoted K_p,q.

  • Regular solids

    You are familiar with at least one of them ... the cube! It is a polyhedron with 6 faces all the same (they're all squares). Figures with all sides the same are called 'regular', so a cube is a regular 6-sided polyhedron.

  • Euclidean and Non-Euclidean geometry

    Note: Euclid's parallel postulate states the following: "For every line l and for every external point P, there exists a unique line through P that is parallel to l." C.

  • Trigonometry Questions

    The radius for the first point is given in the problem - 6. That means that, since this is a regular polygon, the radii are the same for all the other vertices. So, in degrees, the vertices are: (6, 0) (6, 40) (6, 120) etc.

  • Tangents, Nautical Miles and Polar Coordinates of a Nonagon

    (c) For values close to 900, the tan values are extremely high, close to infinity but finite, depending on the precision of the calculator. 2. A nautical mile depends on latitude. It is defined as length of a minute of arc of the earth's radius.

  • graph of tangent function and polar coordinates of nonagon

    Consider the graph of y = tan x. (a) How does it show that the tangent of 90 degrees is undefined? (b) What are other undefined x values?

View More Related Solutions