Handbook of Product Graphs, Second Edition
Handbook of Product Graphs, Second Edition
复制标题
DOI：
10.1201/b10959
复制
发表时间：
2011-06
期刊：
影响因子：
--
通讯作者：
R. Hammack;W. Imrich;S. Klavžar
中科院分区：
文献类型：
--
作者：
R. Hammack;W. Imrich;S. Klavžar
手册的产品图，第二版检查产品的结构和他们的子图之间的二分法。它还设计了有效的算法来识别产品及其子图，并探索了产品的图参数与因子之间的关系。广泛修订和扩展，手册提出了许多重要结果的充分证明，以及最新的研究和猜想。结果和算法新到第二版：消去结果部分立方体的二次识别算法强等距维数结果正则等距嵌入计算Wiener指数连通性结果Hedetniemis猜想的分数版本顶点传递图笛卡尔幂的独立数的结果弦图Vizings猜想的验证最小环基的结果如完整的未成年人和无处零流这个经典手册的第二版提供了一个彻底的介绍，主题和广泛的调查领域。前三部分详细介绍了图书封面图产品。作者讨论了代数性质，如因式分解和消去，并探索了有趣和重要的子图类。第四部分给出了图的乘积和相关类的识别算法。最后两部分着重于图不变量和无限图、有向图和类积图。所选算法的示例实现和其他信息可在图书网站上获得，可通过作者的主页访问。
Handbook of Product Graphs, Second Edition examines the dichotomy between the structure of products and their subgraphs. It also features the design of efficient algorithms that recognize products and their subgraphs and explores the relationship between graph parameters of the product and factors. Extensively revised and expanded, the handbook presents full proofs of many important results as well as up-to-date research and conjectures. Results and Algorithms New to the Second Edition: Cancellation results A quadratic recognition algorithm for partial cubes Results on the strong isometric dimension Computing the Wiener index via canonical isometric embedding Connectivity results A fractional version of Hedetniemis conjecture Results on the independence number of Cartesian powers of vertex-transitive graphs Verification of Vizings conjecture for chordal graphs Results on minimum cycle bases Numerous selected recent results, such as complete minors and nowhere-zero flows The second edition of this classic handbook provides a thorough introduction to the subject and an extensive survey of the field. The first three parts of the book cover graph products in detail. The authors discuss algebraic properties, such as factorization and cancellation, and explore interesting and important classes of subgraphs. The fourth part presents algorithms for the recognition of products and related classes of graphs. The final two parts focus on graph invariants and infinite, directed, and product-like graphs. Sample implementations of selected algorithms and other information are available on the books website, which can be reached via the authors home pages.