By Guo L.-T.

Similar graph theory books

A Beginner's Guide to Discrete Mathematics

Wallis's e-book on discrete arithmetic is a source for an introductory path in an issue primary to either arithmetic and computing device technological know-how, a path that's anticipated not just to hide sure particular themes but additionally to introduce scholars to special modes of inspiration particular to every self-discipline .

Geometric Methods in Bio-Medical Image Processing

The genesis of this ebook is going again to the convention held on the college of Bologna, June 1999, on collaborative paintings among the collage of California at Berkeley and the collage of Bologna. The e-book, in its current shape, is a compilation of a few of the new paintings utilizing geometric partial differential equations and the extent set method in scientific and biomedical snapshot research.

Visualization for Computer Security: 5th International Workshop, VizSec 2008, Cambridge, MA, USA, September 15, 2008. Proceedings

This e-book constitutes the refereed court cases of the fifth foreign Workshop on Visualization for Cyber safety hung on September 15, 2008, in Cambridge, Massachusetts, united states, along with the eleventh overseas Symposium on fresh Advances in Intrusion Detection (RAID). The 18 papers provided during this quantity have been conscientiously reviewed and chosen from 27 submissions.

Extra info for 3-restricted connectivity of graphs with given girth

Example text

Vn such that first come the elements of O1 , followed by the elements of O2 and so on. Let A be the corresponding adjacency matrix of G. Let |Oi | = ni . Suppose that λ is an eigenvalue of R and let x = (x1 , . . , xr )t be a corresponding eigenvector of λ. Let x∗ be the n-vector obtained from x by consecutively repeating ni times each xi . Prove that x∗ is an eigenvector of A with eigenvalue λ. (c) Deduce that the characteristic polynomial of R divides that of A. (d) Deduce that if Aut(G) is nontrivial, then the characteristic polynomial of G is reducible over Z.

For example, α 4 β maps vertex 53 to vertex 1. However, the graph is not vertex-transitive because from an odd-numbered vertex it is possible to have three different paths of length 4 joining the vertex to some other common vertex (for example, vertex 1 to vertex 5), but this is not possible from an even-numbered vertex. Another way to show that the Gray Graph is not vertex-transitive is to consider the distance sequences of its vertices [166]. The distance sequence of a vertex v is the vector (a0 , a1 , .

1. 2. A Cayley colour graph of D4 A colour preserving automorphism of Col( , X) is a permutation π of V(Col( , X)) = such that, for all α, β ∈ , (α, β) is an arc coloured σ if and only if (π(α), π(β)) is also an arc coloured σ . The set of all colour preserving automorphisms of Col( , X) forms a group under composition of functions, and it is denoted by Aut(Col( , X)). 1 Let be a nontrivial finite group with a generating set X. Let π be a permutation of V(Col( , X)). Then π is a colour preserving automorphism of Col( , X) if and only if π(ασ ) = π(α)σ for all α ∈ and σ ∈ X.