Distance-Regular Graphs

By A. Hora, N. Obata. 2007

1,706 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/543b6e474fd7a1d12c0878ae5395ed1e06ff317c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Hongwei Wang
2. Pan Li
3. Yanbang Wang
4. Ralf Koetter
5. Jure Leskovec
6. Frank R. Kschischang
7. G. Exoo
8. E. V. Dam

Citations in the corpus

• Pseudo-random Graphs (2005, unknown): “One can also show (see [1]) that the number of spanning trees t(G) in super (p, ε)-regular graphs satisfies: (p− 2ε)n−1nn−2 ≤ t(G) ≤ (p+ 2ε)n−1nn−2, for small enough ε > 0 and large enough n.”
• Some problems on Cayley graphs (2008, background): “The converse is not true in general (for details see [14]).”
• Dual polar graphs, the quantum algebra U_q(sl_2), and Leonard systems of dual q-Krawtchouk type (2012, background): “For more information we refer the reader to [2, 4, 10, 22].”
• MaxCut in ${\bm H)$-Free Graphs (2005, unknown): “See [11], [19] for more details.”
• Coding for Errors and Erasures in Random Network Coding (2007, background): “Lemma 13 If { ( α 1 , β 1 ) , . . . , ( α r , β r ) } ⊆ W is a collection of r linearly independent elements satisfying β i = f ( α i ) for some linearized polynomial f over F , then { α 1 , . . . , α r } is a linearly independent set.”
• Dynamic Cage Survey (2011, background): “The four (5, 5)-cages have order 30 [66, 29].”
• Eigenvalues and edge-connectivity of regular graphs (2010, background): “Using the results of [3] page 130, we observe that P5(x) equals the characteristic polynomial of the following matrix:”
• A new family of distance-regular graphs with unbounded diameter (2005, methodology): “[6] and the references therein) with respect to an (e− 1)-dimensional subspace is different from the Terwilliger algebra with respect to an (e + 1)dimensional subspace.”
• Distance Encoding: Design Provably More Powerful Neural Networks for Graph Representation Learning (2020, methodology): “We provide the definition of DRG as follows while we refer interested readers to check more properties of DRGs in [35].”