A spectral characterization of the s--clique extension of the square grid graphs.pdf

1、This thesis focuses simultaneously on two problems in spectral graph theory,known as spectral characterization of graphs and characterization of distance regular graphs from their intersection arrays.In particular,we sho

2、w that any co-edge-regular graph which is cospectral with the s-clique extension of the t×t-grid is the s-clique extension of the t×t-grid,if t≥11(s+1)3(s+2),(s≥2).Gavrilyuk and Koolen used a weaker version of this resul

3、t to show that the Grassmann graph Jq(2D,D)is determined by its intersection array as a distance-regular graph,if D＞20and if q≥9,then D＞7.This thesis consist on four chapters and are organized as follows:
　　In Chapter

4、1,we discuss the origin and motivation of our research.Known results are provided to understand its importance.Chapter2focuses on defining all the necessary terminologies and concepts.Certain important concepts such as i

5、nterlacing,equitable partitions,clique extension of square grid graphs are described.An upper bound on the order of a clique in a graph cospectral with the s-clique extension of the square grid graphs,sayΓ,is proved.In C