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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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Automorphisms and regular embeddings of merged Johnson graphs
TL;DR: The automorphism groups of the Johnson graph J(n, m)I are found, and it is deduced that their only regular embedding in an orientable surface is the octahedral map on the sphere for J(4, 2)1, and that they have just six non-orientable regular embeddings.
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Distance-balanced graphs: Symmetry conditions
TL;DR: In this paper, the connection between symmetry properties of graphs and the metric property of being (strongly) distance-balanced is explored, and a complete classification of strongly distancebalanced graphs is given for the following infinite families of generalized Petersen graphs: GP(n,2), GP(5k+1,k), GP (3k+/-3,k) and GP(2k+2,k).
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Distance-regularity and the spectrum of graphs
TL;DR: In this article, the spectrum of a distance-regular graph with diameter 3 and μ = 1 was shown to be a distance regular graph, and it was shown that it is distance regular.
The isomorphism problem for circulant graphs via Schur ring theory.
TL;DR: The developed machinery allows us to give proofs of two eonjectures about necessary conditions on isomorphisms of the cireulants, which show the feasibility of the teehnique of Schur rings in algebraic combinatorics.
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On bijections that preserve complementarity of subspaces
Andrea Blunck,Hans Havlicek +1 more
TL;DR: In this article, the authors consider bijections from G onto G, where G arises from a 2m-dimensional vector space V and if such a bijection @f and its inverse leave one of the relations from above invariant, then also also the other.
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.