algebraic graph theory

plural algebraic graph theories

1. uncountablegraph theoryThe 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.

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

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

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

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

   Graphs with diameter d and girth 2d#43;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.

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

2. countableapplied mathematicsA theory developed by applying algebraic graph theory to a particular problem or application.

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

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

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   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.

   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.