Quadratic Embedding of Graphs
暫譯: 圖的二次嵌入

Obata Nobuaki

Quadratic Embedding of Graphs
  • 出版商: World Scientific Pub
  • 出版日期: 2026-10-08
  • 售價: $4,880
  • 貴賓價: 9.5 折 $4,636
  • 語言: 英文
  • 頁數: 330
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 9819827531
  • ISBN-13: 9789819827534
  • 相關分類: 離散數學 Discrete-mathematics

    • 海外代購書籍(需單獨結帳)

商品描述

This groundbreaking book is the first comprehensive resource dedicated to the Quadratic Embedding Constant (QEC), the novel numeric invariant that precisely bridges combinatorial graph theory and Euclidean distance geometry. Written by the creator of the QEC, the text presents a systematic and in-depth study of how graphs can be characterized and classified through this invariant, with particular emphasis on its behavior under graph operations such as Star Products and Graph Joins.

Discover how the QEC arises directly from Schoenberg's foundational result - that a graph admits a Quadratic Embedding (QE) if its distance matrix is conditionally negative definite. Learn about the wider significance of QE, which is rooted in Menger's work and appears in harmonic analysis of discrete groups and quantum probability. Furthermore, gain deep insight into distance spectra (distance matrix eigenvalues) and the way the QEC interlaces the largest and second largest eigenvalues.

This self-contained and accessible text is perfect for both non-experts and advanced researchers.

商品描述(中文翻譯)

這本開創性的著作是第一本專門全面介紹 Quadratic Embedding Constant（QEC，二次嵌入常數）的資源。QEC 是一種新穎的數值不變量，精確地連結了組合圖論與 Euclidean distance geometry（歐幾里得距離幾何）。本書由 QEC 的創始人撰寫，系統且深入地探討如何透過這項不變量來描述與分類圖，並特別著重於 QEC 在 Star Products（星乘積）與 Graph Joins（圖聯結）等圖運算下的行為。

了解 QEC 如何直接源自 Schoenberg 的奠基性結果：當圖的距離矩陣是 conditionally negative definite（條件負定）時，該圖便具備 Quadratic Embedding（QE，二次嵌入）。探索 QE 更廣泛的意義：它根植於 Menger 的研究，並出現在離散群的調和分析與量子機率之中。此外，深入認識 distance spectra（距離譜，即距離矩陣的特徵值），以及 QEC 如何交錯於最大與次大特徵值之間。

本書內容自成一體、易於理解，非常適合非專業讀者與進階研究人員閱讀。

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