Graph Theory and Applications: With Exercises and Problems by Jean-Claude Fournier

By Jean-Claude Fournier

Content material:
Chapter 1 uncomplicated strategies (pages 21–43):
Chapter 2 timber (pages 45–69):
Chapter three colours (pages 71–82):
Chapter four Directed Graphs (pages 83–96):
Chapter five seek Algorithms (pages 97–118):
Chapter 6 optimum Paths (pages 119–147):
Chapter 7 Matchings (pages 149–172):
Chapter eight Flows (pages 173–195):
Chapter nine Euler excursions (pages 197–213):
Chapter 10 Hamilton Cycles (pages 26–236):
Chapter eleven Planar Representations (pages 237–245):
Chapter 12 issues of reviews (pages 247–259):
Chapter A Expression of Algorithms (pages 261–265):
Chapter B Bases of Complexity conception (pages 267–276):

Show description

Read Online or Download Graph Theory and Applications: With Exercises and Problems PDF

Similar graph theory books

Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations

Partial differential equations and variational tools have been brought into photo processing approximately 15 years in the past, and in depth examine has been conducted given that then. the most aim of this paintings is to provide the range of picture research functions and the best arithmetic concerned. it really is meant for 2 audiences.

Spatio-temporal Networks: Modeling and Algorithms

Spatio-temporal networks (STN)are spatial networks whose topology and/or attributes swap with time. those are encountered in lots of serious components of daily life reminiscent of transportation networks, electrical strength distribution grids, and social networks of cellular clients. STN modeling and computations elevate major demanding situations.

Graph Theory and Applications: With Exercises and Problems

Content material: bankruptcy 1 easy suggestions (pages 21–43): bankruptcy 2 timber (pages 45–69): bankruptcy three hues (pages 71–82): bankruptcy four Directed Graphs (pages 83–96): bankruptcy five seek Algorithms (pages 97–118): bankruptcy 6 optimum Paths (pages 119–147): bankruptcy 7 Matchings (pages 149–172): bankruptcy eight Flows (pages 173–195): bankruptcy nine Euler excursions (pages 197–213): bankruptcy 10 Hamilton Cycles (pages 26–236): bankruptcy eleven Planar Representations (pages 237–245): bankruptcy 12 issues of reviews (pages 247–259): bankruptcy A Expression of Algorithms (pages 261–265): bankruptcy B Bases of Complexity thought (pages 267–276):

Linear Algebra, Third Edition: Algorithms, Applications, and Techniques

Key Features
Introduces deductive reasoning and is helping the reader strengthen a facility with mathematical proofs
Provides a balanced method of computation and thought by way of providing computational algorithms for locating eigenvalues and eigenvectors
Offers very good workout units, starting from drill to theoretical/challeging in addition to helpful and engaging functions no longer present in different introductory linear algebra texts

In this attractive and well-written textual content, Richard Bronson begins with the concrete and computational, and leads the reader to a call of significant purposes. the 1st 3 chapters deal with the fundamentals: matrices, vector areas, and linear differences. the subsequent 3 conceal eigenvalues, Euclidean internal items, and Jordan canonical kinds, delivering probabilities that may be adapted to the instructor's style and to the size of the path. Bronson's method of computation is sleek and algorithmic, and his conception is fresh and easy. all through, the perspectives of the speculation provided are huge and balanced and key fabric is highlighted within the textual content and summarized on the finish of every bankruptcy. The e-book additionally comprises considerable routines with solutions and hints.

Prerequisite: 365 days of calculus is recommended.

Readership: Sophomore- and junior- point scholars in introductory linear algebra

Extra resources for Graph Theory and Applications: With Exercises and Problems

Sample text

In order to merge lists, it is practical to implement them as linked lists, these fusions then being done by simple assignments of pointers. It is necessary to know for each vertex the list in which this vertex lies in order to apply the preceding criteria. This last point makes it necessary, when merging two lists, to go through one of them, the one going into the other, to update the list number of its vertices (the lists being assumed to be numbered). Since Trees 59 we must go through one of the two lists, it is advantageous, for complexity, to choose to go through the shorter of the two lists.

1), of T linking x and y, which ends the proof. ). 9. Given a spanning tree T of G and an edge e of G which does not belong to T , the spanning subgraph T + e contains only one cycle. Proof. 8. If the edge e belonged to two distinct cycles, we could deduce in T two distinct paths linking its endvertices x and y, considering these cycles deprived of the edge e. 3. 2 (Exchange lemma). Given a spanning tree T of G, an edge e of G which does not belong to T and an edge f of the cycle of T + e, then T + e − f is a spanning tree of G.

9. 43 Show that if a bipartite graph G = (X, Y, E) is k-regular then this graph is balanced, that is |X| = |Y | (|X| represents the number of elements of X and similarly for |Y |). 10. (About planar graphs) a) Show that complete graph K4 is planar. Draw it with straight line segments as edges. b) Is complete graph K5 a planar graph? (The answer is no. 11. Given M the adjacency matrix of a graph G whose set of vertices is X = {x1 , x2 , . . , xn }, show that the term (i, j) of M k , the kth power of matrix M , where k is an integer ≥ 1, is the number of walks which link the vertices xi and xj in G.

Download PDF sample

Rated 4.80 of 5 – based on 17 votes