ALGEBRAIC GRAPH THEORY (Graduate Texts in Mathematics 207) By CHRIS GODSIL and GORDON ROYLE: 439 pp., £30.50, ISBN 0-387-95220-9 (Springer, New York, 2001).
By Peter Rowlinson. 2002
421 citations recorded by the source corpus.
Subfields: Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/45c20cb40e1e7f3c32a5189732810fca5e8d8868
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In Computational Theory and Mathematics
- Nikhil Srivastava
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Citations in the corpus
- The critical group of a threshold graph (2002, background): “The order of K(G) is the number of spanning forests in G, and it has a close connection with the Laplacian matrix of G, Kirchoff’s matrix-tree theorem, and a chip-firing game on G (also known as abelian sandpiles in the physics literature) -see [2, 4, 5, 7].”
- Fast linear iterations for distributed averaging (2003, methodology): “The Laplacian matrix is a useful tool in algebraic graph theory, and its eigenstructure reveals many important properties of the graph (see, e.g., [17] [24]).”
- Estimating the Spectral Density of Large Implicit Matrices (2018, background): “For a more detailed discussion of Kneser graphs, see Godsil and Royle (2001).”
- Bounds on graph eigenvalues II (2006, background): “Inequality (1) holds if G has n − 2 vertices of degree n − 1 and 2 vertices of degree n − 2.”
- Semi-Global Leader-Following Consensus of Linear Multi-Agent Systems With Input Saturation via Low Gain Feedback (2013, background): “Moreover, if is a connected graph, then [48].”
- Information processing in complex networks: Graph entropy and information functionals (2008, methodology): “To introduce the novel definitions, we first repeat some basic graph-theoretical preliminaries [5,17,20,31].”
- Graph sparsification by effective resistances (2008, background): “If q = 4C2n log n/ 2, where C is the constant in Lemma 5, then with probability at least 1/2: ∀x ∈ Rn (1− )xT Lx ≤ xT L̃x ≤ (1 + )xT Lx. (2) Sparsifiers that satisfy this condition preserve many properties of the graph.”