algebraic graph theory

English

Noun

algebraic graph theory (countable and uncountable, plural algebraic graph theories)

1. (uncountable, mathematics, graph theory) The subbranch of graph theory in which algebraic methods are applied to problems about graphs.

   The three main branches of algebraic graph theory involve the use of linear algebra, the use of group theory and the study of graph invariants.

   • 1979, Béla Bollobás, Graph Theory: An Introductory Course, Springer, page 26:

     The last section introduces elementary algebraic graph theory which is then applied to electrical networks.

   • 1993, Norman Biggs, Algebraic Graph Theory, 2nd edition, Cambridge University Press, page 38:

     Several famous results in algebraic graph theory, including one of the oldest, are formulae for the numbers of spanning trees of certain graphs.

   • 2013, Chris Godsil, Gordon F. Royle, Algebraic Graph Theory, Springer, page 77:

     Graphs with diameter $d$ and girth $2d+1$ are known as Moore graphs. They were introduced by Hoffman and Singleton in a paper that can be viewed as one of the prime sources of algebraic graph theory.

2. (countable, applied mathematics) A theory developed by applying algebraic graph theory to a particular problem or application.
   • 1999, B. Kumar, B. H. V. Topping, Developments in Analysis and Design Using Finite Element Methods, Civil-Comp Press, page 25,

     Recently hybrid methods are proposed by Kaveh [2] and Kaveh et al. [18] which employ graph and algebraic graph theories simultaneously for domain decomposition of FE meshes and their nodal ordering.

   • 2017, Danwei Wang, Baolin Wu, Eng Kee Poh, Satellite Formation Flying, Springer, page 102:

     [A] decentralized continuous formation keeping approach using local relative measurements is proposed based on algebraic graph theories.

   • 2019, Zhi-Hong Guan, Bin Hu, Xuemin (Sherman) Shen, Introduction to Hybrid Intelligent Networks, Springer, page 22,

     Mathematical tools such as hybrid dynamical systems, complex networks, differential equations, and algebraic graph theories are introduced for modeling and analyzing the hybrid intelligent networks.

Translations

branch of graph theory

• Armenian: հանրահաշվական գրաֆների տեսություն (hanrahašvakan grafneri tesutʻyun)
• Finnish: algebrallinen verkkoteoria
• French: théorie algébrique des graphes f
• German: algebraische Graphentheorie f
• Italian: teoria algebrica dei grafi f

Further reading

• Algebraic combinatorics on Wikipedia.Wikipedia
• Graph property on Wikipedia.Wikipedia
  • Algebraic connectivity on Wikipedia.Wikipedia
• Adjacency matrix on Wikipedia.Wikipedia
• Laplacian matrix on Wikipedia.Wikipedia
• Spectral graph theory on Wikipedia.Wikipedia