Name _ Tuesday January 20, 2009 Math 575 Quiz #1 1. Suppose that G is a graph having 28 vertices and 82 edges in which every vertex has degree 5 or degree 7. How many vertices have degree 5? Solution: Suppose that there are f vertices of degree 5 and s ve
April 9, 2009
1. (a). Mengers Theorem states that if v and u are two non-adjacent vertices of a graph, then the
internally disjoint v-u paths
is the same as the
vertices needed to remove to separa
Practice Exam #1A
(a). Neighborhood of a vertex v.
Solution: The neighborhood of a vertex v consists of all the vertices adjacent to v.
(b). Eccentricity of a vertex v in a connected graph G.
Solution: The eccentricity of a vert
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1. (a). Explain the difference between a plane graph and a planar graph.
Solution: A planar graph is one that can be drawn in the plane so that no two
edges cross; A plane graph refers to an actual drawing of a plana
Practice Exam 2B
1. (a). State Taits Conjecture.
Solution: Every 3-connected, cubic planar graph is Hamiltonian.
(b). A graph G is traceable if
Solution: It has a spanning path.
(c). A tournament is an _
Solution: oriented complete graph.
February 20, 2009
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1. Complete the definitions of the following terms.
(a). A graph G is planar if
Solution: it can be drawn in the plane so that no two edges cross except at vertices
of the graph.
(b). The eccentricity