Algebraic Graph Theory

@inproceedings{Godsil2001AlgebraicGT,
  title={Algebraic Graph Theory},
  author={Chris D. Godsil and Gordon F. Royle},
  booktitle={Graduate texts in mathematics},
  year={2001}
}
  • C. GodsilG. Royle
  • Published in Graduate texts in mathematics 20 April 2001
  • Mathematics
Graphs.- Groups.- Transitive Graphs.- Arc-Transitive Graphs.- Generalized Polygons and Moore Graphs.- Homomorphisms.- Kneser Graphs.- Matrix Theory.- Interlacing.- Strongly Regular Graphs.- Two-Graphs.- Line Graphs and Eigenvalues.- The Laplacian of a Graph.- Cuts and Flows.- The Rank Polynomial.- Knots.- Knots and Eulerian Cycles.- Glossary of Symbols.- Index. 
View via Publisher
link.springer.com
8,883 Citations
Highly Influential Citations
480
Background Citations
3,516
Methods Citations
674
Results Citations
43

8,883 Citations

Algebraic Graph Theory: Automorphism Groups and Cayley graphs

An algebraic approach to graph theory can be useful in numerous ways. There is a relatively natural intersection between the fields of algebra and graph theory, specifically between group theory and…

Quotient-polynomial graphs

Strongly regular edge-transitive graphs

It is shown that the irreducible graphs in this family have quasiprimitive automorphism groups, and it is proved (using the Classification of Finite Simple Groups) that no graph in thisfamily has a holomorphic simple automorphisms group.

Cayley graphs and G-graphs: Some applications

Normal Edge-Transitive Cayley Graphs of the Group

A Cayley graph of a group is called normal edge-transitive if the normalizer of the right representation of the group in the automorphism of the Cayley graph acts transitively on the set of edges of…

On Generalizations of the Petersen Graph and the Coxeter Graph

  • M. Orel
  • Mathematics
    Electron. J. Comb.
  • 2015
Two related infinite families of graphs are considered, which generalize the Petersen and the Coxeter graph, and it is determined which of these graphs are vertex/edge/arc-transitive or distance-regular.

A note on coset graphs

Coset graphs are a generalization of Cayley graphs. They arise in the construction of graphs and digraphs with transitive automorphism groups. Moreover, the consideration of coset graphs makes it…

Tetravalent vertex-transitive graphs of order $6p$

A graph is vertex-transitive if its automorphism group acts transitively on vertices of the graph. A vertex-transitive graph is a Cayley graph if its automorphism group contains a subgroup acting…

Distance-regular Cayley graphs with least eigenvalue $$-2$$-2

The possible connection sets for the lattice graphs are classified and some results on the structure of distance-regular Cayley line graphs of incidence graphs of generalized polygons are obtained.

5-Arc transitive cubic Cayley graphs on finite simple groups

...

References

SHOWING 1-7 OF 7 REFERENCES

The Connectivity of Strongly Regular Graphs

The Erdös-Ko-Rado theorem for vector spaces

The exact bound in the Erdös-Ko-Rado theorem

The bound (t+1)(k-t-1) represents the best possible strengthening of the original 1961 theorem of Erdös, Ko, and Rado which reaches the same conclusion under the hypothesisn≧t+(k−t) .

Optimal state-determination by mutually unbiased measurements

INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS

2. Notation The letters a, b, c, d, x, y, z denote finite sets of non-negative integers, all other lower-case letters denote non-negative integers. If fc I, then [k, I) denotes the set…

An Erdos-Ko-Rado theorem for the derangement graph of PGL(2,q) acting on the projective line

  • An Erdos-Ko-Rado theorem for the derangement graph of PGL(2,q) acting on the projective line

Algebraic Graph Theory, Springer-Verlag, (New York)

  • 2001