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By Sriram V. Pemmaraju, Steven S. Skiena

With examples of all 450 features in motion plus instructional textual content at the arithmetic, this publication is the definitive advisor to Experimenting with Combinatorica, a usual software program package deal for instructing and study in discrete arithmetic. 3 fascinating sessions of workouts are provided--theorem/proof, programming routines, and experimental explorations--ensuring nice flexibility in instructing and studying the cloth. The Combinatorica person group levels from scholars to engineers, researchers in arithmetic, laptop technological know-how, physics, economics, and the arts. Recipient of the EDUCOM larger schooling software program Award, Combinatorica is incorporated with each replica of the preferred machine algebra procedure Mathematica.

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Extra resources for Computational discrete mathematics: combinatorics and graph theory with Mathematica

Example text

A maximum clique is a complete subgraph with maximum number of vertices. Computing a maximum clique is not just NP-hard; it is hard even to approximate to any reasonable factor [ALM+92]. 7]; ArticulationVertices Automorphisms Backtrack BiconnectedComponents Bridges ChromaticNumber ChromaticPolynomial Conne ctedComponent s DegreeSequence Degrees Degrees0f2Neighborhood Diameter Distances Eccentricity EdgeChromaticNuraber EdgeColoring EdgeConnectivity Equivalences EulerianCycle Girth GraphCenter GraphPolynomial HarailtonianCycle Combinoforico functions for graph invariants.

This can be easily shown to be true in general whenever edge weights satisfy the triangle inequality. 2 Graph Theory and Algorithms Cayley proved that the number of spanning trees of a complete graph is In[87]:= NumberOfSpanningTrees[CompleteGraph[10]] wn-2 0ut[87]= 100000000 Assuming unit capacities, n ~ 1 units of flow can be pushed from one vertex to another in a complete graph with n vertices. In[88]:~ NetvorkFlov[CompleteGraph[7], 1, 7] More information can be obtained by providing the tag Edge to the function.

A graph object can constructed by hand and explicitly typed out and provided to functions. Here is an example. However, we discourage this because the user has to make sure that the syntax for the various pieces in the graph is carefully observed. For example, edges and vertices have an extra set of parentheses around them. Also, edges in an undirected graph must be listed as {i,j], where i < j. Instead, we recommend using a function such as FromUnorderedPairs to construct a graph. The function will perform some syntax checking and allows the user some flexibility in specifying the graph.

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