(5) Sketch K1,5 and determine the longest cycle that covers all the vertices.
Let G be a graph in which there is a cycle C odd length that has vertices on all of the other odd cycles. Prove that the chromatic number of G is less than or equal to 5.
(7) Sketch any connected 3-regular Graph G with 6 vertices, determine how many edges must be removed to produce a Spanning Tree and then sketch any Spanning Tree.
Sketch a tree T with 10 vertices where 4 vertices have degree 3 and 6 vertices have degree 1.
The cycle index polynomial for the rotation group of (the vertices of) the dodecahedron is 1S 60 Ci Match each of the terms with the following { identity, rotation about face centres., rotation about edge centres, rotation about vertices . Explain The cycle index polynomial for the rotation group of (the vertices of) the dodecahedron is 1S 60 Ci Match each of the terms with the following { identity, rotation about face centres., rotation about edge centres, rotation about vertices...
4. 5. (a) Sketch the region bounded by y- +2x-4, y-x2+4x-4 clearly indicating vertices on the graph, (b) Draw the area element AA on the graph and find a general expression for A4. (c) Set up a definite integral for A and find the area. 4. 5. (a) Sketch the region bounded by y- +2x-4, y-x2+4x-4 clearly indicating vertices on the graph, (b) Draw the area element AA on the graph and find a general expression for A4. (c) Set...
2. Sketch the phosphorus cycle. Include all inputs and major forms of phosphorus, and label all reactions. Why is phosphorus typically the limiting nutrient in aquatic systems?
For the following ellipse: find the center, vertices, foci. Sketch the graph.
Sketch the graph of the following hyperbola. Specify the coordinates of the vertices and foci, and find the equations of the asymptotes. Use a graphing utility to check your work. y² x² 36 = 1 25 The vertices of the hyperbola arı (Type an ordered pair. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) The foci of the hyperbola are (Type an ordered pair. Type an exact answer, using radicals as needed....
The cycle index polynomial for the rotation group of (the vertices of) the dodecahedron is 1S 60 Ci Match each of the terms with the following { identity, rotation about face centres., rotation about edge centres, rotation about vertices . Explain
1. For each of the figures below, determine the group of rigid motions. Express all elements of the group as permutations of the vertices, written in disjoint cycle notation. Square with 2 line connecting opposite vertices 3 Equilateral triangle. 3 1. For each of the figures below, determine the group of rigid motions. Express all elements of the group as permutations of the vertices, written in disjoint cycle notation. Square with 2 line connecting opposite vertices 3 Equilateral triangle. 3