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Distance-Regular Graphs
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In this paper, a connected simple graph with vertex set X of diameter d is considered, and the authors define Ri X2 by (x, y) Ri whenever x and y have graph distance.Abstract:
Consider a connected simple graph with vertex set X of diameter d. Define Ri X2 by (x, y) Ri whenever x and y have graph distanceread more
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On the additive (/spl Zopf//sub 4/-linear and non-/spl Zopf//sub 4/-linear) Hadamard codes: rank and kernel
TL;DR: All the possible nonisomorphic additive Hadamard codes are characterized and the rank and the dimension of the kernel are computed for each one.
Journal ArticleDOI
Metric dimension of some distance-regular graphs
Jun Guo,Kaishun Wang,Fenggao Li +2 more
TL;DR: This paper constructs a resolving set of Johnson graphs, doubled Odd graph, doubled Grassmann graphs and twisted Grassmann graph, respectively, and obtains the upper bounds on the metric dimension of these graphs.
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2-Homogeneous bipartite distance-regular graphs
TL;DR: The 2-homogeneous property of a bipartite distance-regular graph is characterized in three ways: these characterizations involve the intersection numbers, the eigenvalues, and the Krein parameters, respectively.
Journal ArticleDOI
Distance transitive graphs and finite simple groups
TL;DR: In this paper, the first step in the classification of finite primitive distancetransitive graphs was taken and the problem was reduced to the case where the automorphism group is either almost simple or affine.
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Foster's Formulas via Probability and the Kirchhoff Index
TL;DR: In this paper, an elementary identity for the expected hitting times of an ergodic N-state Markov chain which yields as a corollary Foster's second formula for electrical networks was established.
References
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Journal ArticleDOI
Equilateral point sets in elliptic geometry
J.H. van Lint,J.J. Seidel +1 more
TL;DR: In this paper, the authors highlight equilateral point sets in elliptic geometry and show that Paley's construction may be reversed to obtain a C -matrix of order 46, in view of the existence of a Hadamard matrix of order 92.
BookDOI
On construction and identification of graphs
TL;DR: The problem of graph identification has been studied in the theory of permutation groups for a long time, see as mentioned in this paper for a discussion of the main points of the problem and an algorithm for graph identification.