A Spectral Characterization of the S-clique Extension of the Square Grid Graphs

作     者：Muhammad Riaz 

作者单位：中国科学技术大学 

学位级别：硕士

导师姓名：Jack H.Koolen

授予年度：2018年

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主      题：Co-edge-regular graph Eigenvalue Few eigenvalues Spectral characterization 

摘      要：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 *** particular,we show 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 result to show that the Grassmann graph Jq（2D,D）is determined by its intersection array as a distance-regular graph,if D20 and if q ≥ 9,then D*** thesis consist on four chapters and are organized as follows:In Chapter 1,we discuss the origin and motivation of our *** results are provided to understand its *** 2 focuses on defining all the necessary termi-nologies and *** important concepts such as interlacing,equitable partitions,clique extension of square grid graphs are *** upper bound on the order of a clique in a graph cospectral with the s-clique extension of the square grid graphs,say（?）,is *** Chapter 3,we present the proof of our *** 4 comprises conclusion and future work.