Results 21 to 30 of about 3,086,920 (343)
A unified view of inequalities for distance-regular graphs, part I
J. Comb. Theory B, 2020 In this paper, we introduce the language of a configuration and of t-point counts for distance-regular graphs (DRGs). Every t-point count can be written as a sum of ( t − 1 ) -point counts.
A. Neumaier, Safet Penjić
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Arithmetic completely regular codes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 In this paper, we explore completely regular codes in the Hamming graphs and related graphs. Experimental evidence suggests that many completely regular codes have the property that the eigenvalues of the code are in arithmetic progression.
Jacobus Koolen +3 more
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Linear codes and cyclic codes over finite rings and their generalizations: a survey
Electronic Journal of Graph Theory and Applications, 2023 We survey a recent progress of cyclic codes over finite rings and their generalization to skew cyclic as well as skew cyclic codes with derivation over finite rings, focusing on structural properties of the codes.
Djoko Suprijanto
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Non-Bipartite Distance-Regular Graphs with a Small Smallest Eigenvalue [PDF]
Electronic Journal of Combinatorics, 2019 In 2017, Qiao and Koolen showed that for any fixed integer $D\geqslant 3$, there are only finitely many such graphs with $\theta_{\min}\leqslant -\alpha k$, where ...
Zhi Qiao, Yi-Fan Jing, J. Koolen
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Some Resolving Parameters in a Class of Cayley Graphs
Journal of Mathematics, 2022 Resolving parameters are a fundamental area of combinatorics with applications not only to many branches of combinatorics but also to other sciences.
Jia-Bao Liu, Ali Zafari
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On a certain class of 1-thin distance-regular graphs
Ars Math. Contemp., 2020 Let Γ denote a non-bipartite distance-regular graph with vertex set X , diameter D ≥ 3 , and valency k ≥ 3 . Fix x ∈ X and let T = T ( x ) denote the Terwilliger algebra of Γ with respect to x . For any z ∈ X and for 0 ≤ i ≤ D , let Γ i ( z ) =
Mark S. MacLean, Štefko Miklavič
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On the spectral gap and the automorphism group of distance-regular graphs [PDF]
J. Comb. Theory B, 2019 We prove that a distance-regular graph with a dominant distance is a spectral expander. The key ingredient of the proof is a new inequality on the intersection numbers. We use the spectral gap bound to study the structure of the automorphism group.
Bohdan Kivva
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Using symbolic computation to prove nonexistence of distance-regular graphs [PDF]
Electronic Journal of Combinatorics, 2018 A package for the Sage computer algebra system is developed for checking feasibility of a given intersection array for a distance-regular graph. We use this tool to show that there is no distance-regular graph with intersection array$$\{(2r+1)(4r+1)(4t-1)
J. Vidali
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ON SOME VERTEX-TRANSITIVE DISTANCE-REGULAR ANTIPODAL COVERS OF COMPLETE GRAPHS
Ural Mathematical Journal, 2022 In the present paper, we classify abelian antipodal distance-regular graphs \(\Gamma\) of diameter 3 with the following property: \((*)\) \(\Gamma\) has a transitive group of automorphisms \(\widetilde{G}\) that induces a primitive almost simple ...
Ludmila Yu. Tsiovkina
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The smallest eigenvalues of Hamming graphs, Johnson graphs and other distance-regular graphs with classical parameters [PDF]
J. Comb. Theory B, 2017 We prove a conjecture by Van Dam and Sotirov on the smallest eigenvalue of (distance-$j$) Hamming graphs and a conjecture by Karloff on the smallest eigenvalue of (distance-$j$) Johnson graphs.
A. Brouwer +3 more
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