Script 2013W 104.271 Discrete Mathematics VO (Gittenberger)
... a local view of the graph and they use these local values to solve the maximization (or minimization) problem. Since these algorithms are greedy, they generally don’t produce optimal maximal or minimal spanning trees. However they always work in the special case of matroids. Using Kruskal’s algorith ...
... a local view of the graph and they use these local values to solve the maximization (or minimization) problem. Since these algorithms are greedy, they generally don’t produce optimal maximal or minimal spanning trees. However they always work in the special case of matroids. Using Kruskal’s algorith ...
Log Functions I
... Justification: The value of f(x) = log 3 x 2 is equivalent to y = 2log 3 x (review the previous question to see its graph). Recall that y = log3(x) is only defined when x is positive. The domain of the log function is x > 0. Since x2 is always positive, the log function f(x) = log3(x2) is defined fo ...
... Justification: The value of f(x) = log 3 x 2 is equivalent to y = 2log 3 x (review the previous question to see its graph). Recall that y = log3(x) is only defined when x is positive. The domain of the log function is x > 0. Since x2 is always positive, the log function f(x) = log3(x2) is defined fo ...
4-2
... Trish can run the 200 m dash in 25 s. The function f(x) = 200 – 8x gives the distance remaining to be run after x seconds. Graph this function and find the intercepts. What does each intercept represent? ...
... Trish can run the 200 m dash in 25 s. The function f(x) = 200 – 8x gives the distance remaining to be run after x seconds. Graph this function and find the intercepts. What does each intercept represent? ...
Exponential and Logarithmic Functions
... EXPONENTIAL AND LOGARITHMIC FUNCTIONS An exponential function is one whose variable is a power or exponent. Any function of the form f (x) = ax , where a is a non-zero positive constant, is an exponential function. The graphs on the right are of two such exponential functions: y = 2x and y = 5x. All ...
... EXPONENTIAL AND LOGARITHMIC FUNCTIONS An exponential function is one whose variable is a power or exponent. Any function of the form f (x) = ax , where a is a non-zero positive constant, is an exponential function. The graphs on the right are of two such exponential functions: y = 2x and y = 5x. All ...
Connectivity, Devolution, and Lacunae in
... and are called geometric random graphs. In recent years these models have seen renewed interest spurred by applications in computational geometry, randomly deployed sensor networks, and cluster analysis; see the monograph by Penrose for a slew of references [6]. The digraph induced by a general mosa ...
... and are called geometric random graphs. In recent years these models have seen renewed interest spurred by applications in computational geometry, randomly deployed sensor networks, and cluster analysis; see the monograph by Penrose for a slew of references [6]. The digraph induced by a general mosa ...
quadratic - James Tanton
... There is a reason why the “cubic formula” is not taught in schools. It’s somewhat tricky. Let’s develop the formula here through a series of exercises. Consider an equation of the form: x 3 + Ax 2 + Bx + C = 0 . ...
... There is a reason why the “cubic formula” is not taught in schools. It’s somewhat tricky. Let’s develop the formula here through a series of exercises. Consider an equation of the form: x 3 + Ax 2 + Bx + C = 0 . ...
Dual graph
In the mathematical discipline of graph theory, the dual graph of a plane graph G is a graph that has a vertex for each face of G. The dual graph has an edge whenever two faces of G are separated from each other by an edge. Thus, each edge e of G has a corresponding dual edge, the edge that connects the two faces on either side of e.Graph duality is a topological generalization of the geometric concepts of dual polyhedra and dual tessellations, and is in turn generalized algebraically by the concept of a dual matroid. Variations of planar graph duality include a version of duality for directed graphs, and duality for graphs embedded onto non-planar two-dimensional surfaces.However, the notion described in this page is different from the edge-to-vertex dual (line graph) of a graph and should not be confused with it.The term ""dual"" is used because this property is symmetric, meaning that if H is a dual of G, then G is a dual of H (if G is connected). When discussing the dual of a graph G, the graph G itself may be referred to as the ""primal graph"". Many other graph properties and structures may be translated into other natural properties and structures of the dual. For instance, cycles are dual to cuts, spanning trees are dual to the complements of spanning trees, and simple graphs (without parallel edges or self-loops) are dual to 3-edge-connected graphs.Polyhedral graphs, and some other planar graphs, have unique dual graphs. However, for planar graphs more generally, there may be multiple dual graphs, depending on the choice of planar embedding of the graph. Testing whether one planar graph is dual to another is NP-complete.