{"product_id":"the-mutually-beneficial-relationship-of-graphs-and-matrices-9781470437220","title":"The Mutually Beneficial Relationship of Graphs and Matrices","description":"\u003cp\u003e • Author(s): Richard A. Brualdi\u003cbr\u003e • Publisher: Orient Blackswan Pvt Ltd\u003cbr\u003e • Publisher Imprint: Orient Blackswan Pvt Ltd\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp style=\"text-align: justify\"\u003eGraphs and matrices enjoy a fascinating and mutually beneficial relationship. This interplay has benefited both graph theory and linear algebra. In one direction, knowledge about one of the graphs that can be associated with a matrix can be used to illuminate matrix properties and to get better information about the matrix. Examples include the use of digraphs to obtain strong results on diagonal dominance and eigenvalue inclusion regions and the use of the Rado-Hall theorem to deduce properties of special classes of matrices. Going the other way, linear algebraic properties of one of the matrices associated with a graph can be used to obtain useful combinatorial information about the graph. The adjacency matrix and the Laplacian matrix are two well-known matrices associated to a graph, and their eigenvalues encode important information about the graph. Another important linear algebraic invariant associated with a graph is the Colin de Verdière number, which, for instance, characterizes certain topological properties of the graph. \u003c\/p\u003e \u003cp\u003eThis book is not a comprehensive study of graphs and matrices. The particular content of the lectures was\u003cbr\u003e chosen for its accessibility, beauty, and current relevance, and for the possibility of enticing the audience to want to learn more.\u003c\/p\u003e","brand":"Orient Blackswan Pvt Ltd","offers":[{"title":"Paperback","offer_id":45616467083415,"sku":"9781470437220","price":1085.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9781470437220.webp?v=1769294864","url":"https:\/\/atlanticbooks.com\/products\/the-mutually-beneficial-relationship-of-graphs-and-matrices-9781470437220","provider":"Atlantic Books","version":"1.0","type":"link"}