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Christopher David Godsil is a professor and the former Chair at the Department of Combinatorics and Optimization in the faculty of mathematics at the University of Waterloo.He wrote the popular textbook on algebraic graph theory, entitled Algebraic Graph Theory, with Gordon Royle, [1] His earlier textbook on algebraic combinatorics discussed distance-regular graphs and association schemes.
Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph invariants.
Gordon F. Royle is a professor at the School of Mathematics and Statistics at The University of Western Australia. [1]Royle is the co-author (with Chris Godsil) of the book Algebraic Graph Theory (Springer Verlag, 2001, ISBN 0-387-95220-9).
In the mathematical fields of graph theory and combinatorics, a matching polynomial (sometimes called an acyclic polynomial) is a generating function of the numbers of matchings of various sizes in a graph. It is one of several graph polynomials studied in algebraic graph theory.
In the mathematical field of graph theory, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices at distance j from v and at distance k from w depends only upon j, k, and the distance between v and w. Some authors exclude the complete graphs and disconnected graphs from this definition.
Independently of the work in algebraic graph theory, Potts began studying the partition function of certain models in statistical mechanics in 1952. The work by Fortuin and Kasteleyn [ 9 ] on the random cluster model , a generalisation of the Potts model , provided a unifying expression that showed the relation to the Tutte polynomial.
In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance, there is an automorphism of the graph that carries v to x and w to y.
In the mathematical field of graph theory, an automorphism is a permutation of the vertices such that edges are mapped to edges and non-edges are mapped to non-edges. [1] A graph is a vertex-transitive graph if, given any two vertices v 1 and v 2 of G, there is an automorphism f such that