**VERTICES** OF CLOSED CURVES INRIEMANNIAN SURFACES MOHAMMADGHOMI Abstract. We uncover some connections between the topology of a complete Riemannian surface Mandtheminimum number of **vertices**, i.e., critical points of geodesic curvature, of closed curves in M.

Homework6(Exercises for Midterm) Due 5 March 1. If a complete graph has 10 **vertices**. If any vertex can be the starting points, how many hamiltonian circuits does it have?

Teacher's Guide 2B: Unit 14 - Geometry © 2008 Marshall Cavendish International (Singapore) Private Limited 135 Lesson 14.1b Counting Faces, **Vertices** and Edges Objectives ∞ Identify flat and curved faces on 3-dimensional shapes. ∞ Identify **vertices** and edges on 3-dimensional shapes.

On A New Class Of Codes For Identifying **Vertices** In Graphs - Information Theory, IEEE Transactions on

Furman University Electronic Journal of Undergraduate Mathematics Volume 9,1-20,2004 VERTEX-MAGIC DAISYCUNNINGHAM Abstract. This paper addresses labeling graphs in such away that the sum of the vertex labels and incident edge labels are the same for every vertex.

026_73735_C14L4_PS.indd. 1. Draw and name a solid figure that has 5 **vertices**, 5 faces, and 8 edges.

Drawing Graphs with Non-Uniform **Vertices** David Harel harel@wisdom.weizmann.ac.il Yehuda Koren yehuda@wisdom.weizmann.ac.il Dept. of Computer Science and Applied Mathematics

Together with the class, write the number of faces, edges, and **vertices** each three-dimensional shape has. As they explore various solid figures, help them realize that the faces of a solid figure are in the shape of plane figures.

Two graphs are isomorphic * for some ordering of their **vertices** their adjacency matrices are equal. Question . How many different adjacency matrices do a graph with n **vertices** have?

Lesson 4-4 Example 1 Translate a Figure Find the coordinates of the **vertices** of the image of quadrilateral ABCD with A (-4, 1), B (-2, 3), C (0, 0), and D (-4, -3), if it is moved 5 units to the right and 3 units down.