By Steven Skiena, Sriram Pemmaraju

ISBN-10: 0521806860

ISBN-13: 9780521806862

With examples of all 450 features in motion plus educational textual content at the arithmetic, this publication is the definitive advisor to Experimenting with Combinatorica, a commonplace software program package deal for instructing and study in discrete arithmetic. 3 fascinating sessions of routines are provided--theorem/proof, programming routines, and experimental explorations--ensuring nice flexibility in educating and studying the cloth. The Combinatorica consumer neighborhood levels from scholars to engineers, researchers in arithmetic, desktop technological know-how, physics, economics, and the arts. Recipient of the EDUCOM better schooling software program Award, Combinatorica is integrated with each reproduction of the preferred computing device algebra process Mathematica.

Show description

Read Online or Download Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica PDF

Similar graph theory books

Armen H. Zemanian's Graphs and Networks: Transfinite and Nonstandard PDF

This self-contained e-book examines effects on transfinite graphs and networks accomplished via a continuous examine attempt up to now numerous years. those new effects, overlaying the mathematical idea of electric circuits, are assorted from these awarded in formerly released books through the writer, Transfiniteness for Graphs, electric Networks, and Random Walks and Pristine Transfinite Graphs and Permissive electric Networks.

Download PDF by Martin Charles Golumbic: Algorithmic Graph Theory and Perfect Graphs

Algorithmic Graph concept and ideal Graphs, first released in 1980, has turn into the vintage advent to the sector. This new Annals version keeps to exhibit the message that intersection graph versions are an important and critical device for fixing real-world difficulties. It continues to be a stepping stone from which the reader may well embark on one of the attention-grabbing study trails.

Download e-book for iPad: An Introduction to Catalan Numbers by Steven Roman

This textbook presents an advent to the Catalan numbers and their extraordinary houses, in addition to their numerous purposes in combinatorics. Intended to be available to scholars new to the topic, the e-book starts off with extra effortless issues ahead of progressing to extra mathematically refined themes.

Extra resources for Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica

Example text

15. 1. Adjacency matrices and adjacency lists The data structures introduced here are commonly used to represent graphs. In particular, as we shall see later, the use of adjacency lists can make an important contribution to the efficiency of an algorithm. An adjacency matrix for the graph G = (V, E) is an n x n matrix A, such that: A(i,j) = 1 if (i,j) E E = 0 otherwise If G is an undirected graph then A(i,j) = AU, i), whilst if G is a digraph then A is generally asymmetric. 13 illustrates the two cases.

The elements are arranged in partial order, by which we mean that the priority of any vertex is no greater than the priority of its sons. Moreover, the tree is as balanced as possible (path lengths from the root to the leaves differ by at most one) with leaves furthest from the root being arranged to the left. Such a tree is shown opposite (figure (a┬╗. Consider first the operation of removing the item of lowest priority. This item will be located at the root of the tree so that its removal no longer leaves us with a tree.

Before providing an illustration of this algorithm we point out that if v is the root of a DFS tree then for every son Vi of v we have p(v' ) ~ DFI(v). This ensures that whenever v is revisited in a DFS search for blocks, the edges of the block containing (v, v') are removed from the stack. Thus the case when v is both a root and an articulation point is automatically accommodated. 19 shows an application of the depth-first search for blocks algorithm. In (a) the graph subjected to the algorithm is shown as are the spanning-tree, and the values of DFI(v) and P(v) found during the course of computation.

Download PDF sample

Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica by Steven Skiena, Sriram Pemmaraju

by Jason

Rated 4.49 of 5 – based on 33 votes