Results 11 to 20 of about 28,279 (264)
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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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 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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Two distance-regular graphs [PDF]
Journal of Algebraic Combinatorics, 2011 We construct two families of distance-regular graphs, namely the subgraph of the dual polar graph of type B_3(q) induced on the vertices far from a fixed point, and the subgraph of the dual polar graph of type D_4(q) induced on the vertices far from a fixed edge. The latter is the extended bipartite double of the former.
Brouwer, Andries E. +1 more
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Tight Distance-Regular Graphs [PDF]
Journal of Algebraic Combinatorics, 2000 We consider a distance-regular graph $\G$ with diameter $d \ge 3$ and eigenvalues $k=θ_0>θ_1>... >θ_d$. We show the intersection numbers $a_1, b_1$ satisfy $$ (θ_1 + {k \over a_1+1}) (θ_d + {k \over a_1+1}) \ge - {ka_1b_1 \over (a_1+1)^2}. $$ We say $\G$ is {\it tight} whenever $\G$ is not bipartite, and equality holds above.
Jurišić, Aleksandar +2 more
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The Electronic Journal of Combinatorics, 2016 This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A., Distance-Regular Graphs, Springer-Verlag, Berlin,
Edwin R. van Dam +2 more
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D-magic strongly regular graphs
AKCE International Journal of Graphs and Combinatorics, 2020 For a set of distances D, a graph G on n vertices is said to be D-magic if there exists a bijection and a constant k such that for any vertex x, where is the D-neighbourhood set of x.
Rinovia Simanjuntak, Palton Anuwiksa
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Edge-distance-regular graphs are distance-regular
Journal of Combinatorial Theory, Series A, 2013 A graph is edge-distance-regular when it is distance-regular around each of its edges and it has the same intersection numbers for any edge taken as a root. In this paper we give some (combinatorial and algebraic) proofs of the fact that every edge-distance-regular graph $\G$ is distance-regular and homogeneous.
Cámara Vallejo, Marc +4 more
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Characterizing Distance-Regularity of Graphs by the Spectrum [PDF]
SSRN Electronic Journal, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Edwin R. van Dam +3 more
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