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question a what is eulers formula for connected planar graphsb how can eulers formula for planar graphs be used to show
question a describe dijkstras algorithm for finding the shortest path in a weighted graph between two verticesb draw a
question a define a hamilton circuit in a simple graphb give some properties of a simple graph that imply that it does
question a define an euler circuit and an euler path in an undirected graphb describe the famous koumlnigsberg bridge
question a explain how an adjacency matrix can be used to represent a graphb how can adjacency matrices be used to
qusetion a what does it mean for a graph to be connectedb what are the connected components of a
question a what does it mean for two simple graphs to be isomorphicb what is meant by an invariant with respect to
question a describe three different methods that can be used to represent a graphb draw a simple graph with at least
question a what is a bipartite graphb which of the graphs kn cn and wn are bipartitec how can you determine whether an
question show that the coloring produced by this algorithm may use more colors than are necessary to color a graph a
question show that if g is a chromatically k-critical graph then the degree of every vertex of g is at least k - 1a
question frequencies for mobile radio or cellular telephones are assigned by zones each zone is assigned a set of
question show that every planar graph g can be colored using five or fewer colorsthe famous art gallery problem asks
qusetion what is the relationship between the sum of the degrees of the vertices in an undirected graph and the number
question what is the relationship between the sum of the in-degrees and the sum of the out-degrees of the vertices in a
question describe the following families of graphsa kn the complete graph on n verticesb kmn the complete bipartite
question what can be said about the chromatic number of a graph that has kn as a subgraphthis algorithm can be used to
question seven variables occur in a loop of a computer program the variables and the steps during which they must be
question suppose that n devices are on a circuit board and that these devices are connected by colored wires express
question a zoo wants to set up natural habitats in which to exhibit its animals unfortunately some animals will eat
question the mathematics department has six committees each meeting once a month how many different meeting times must
question how many different channels are needed for six stations located at the distances shown in the table if two
question schedule the final exams for math 115 math 116 math 185 math 195 cs 101 cs 102 cs 273 and cs 473 using the
question what is the least number of colors needed to color a map of the united states do not consider adjacent states
question construct the dual graph for the map shown then find the number of colors needed to color the map so that no