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Topology Control in Spherical 3D Sensor Networks. [PDF]

Sensors (Basel)
Zarifis N, Katsaros D.
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Distance-regular graphs

, 1997
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Cubic Distance-Regular Graphs

Journal of the London Mathematical Society, 1986
This paper completes the classification of cubic distance-regular graphs. We define the profile and period of certain cycles in such a graph, and obtain congruence conditions on the periods that help determine the feasible intersection arrays. It turns out that there are just 13 possible cases and in each case the array is realised by a unique graph.
Biggs, N.L., Boshier, A., Shawe-Taylor, J.   +2 more
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On Bounding the Diameter of a Distance-Regular Graph

Combinatorica, 2021
It is investigated how to use an initial portion of the intersection array of a distance-regular graph to give an upper bound for the diameter of the graph. In particular, three new diameter bounds are obtained. These bounds are tight for the Hamming \(d\)-cube, doubled odd graphs, the Heawood graph, Tutte's \(8\)-cage and \(12\)-cage, the generalized ...
Arnold Neumaier, Safet Penjic
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Eigenpolytopes of Distance Regular Graphs

Canadian Journal of Mathematics, 1998
AbstractLet X be a graph with vertex set V and let A be its adjacency matrix. If E is the matrix representing orthogonal projection onto an eigenspace of A with dimension m, then E is positive semi-definite. Hence it is the Gram matrix of a set of |V| vectors in Rm. We call the convex hull of a such a set of vectors an eigenpolytope of X.
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Eigenvectors of Distance-Regular Graphs

SIAM Journal on Matrix Analysis and Applications, 1988
The author studies the set of points the coordinates of which are rows of the matrix in which the columns are orthogonal eigenvectors associated to an eigenvalue of the adjacency matrix of a graph. In particular, the second largest eigenvalue \(\alpha\) and distance-regular graphs G are considered.
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Distance-regular Graphs of the Height h

Graphs and Combinatorics, 1999
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Bounding the diameter of distance-regular graphs

Combinatorica, 1988
Let G be a connected distance regular graph with valence \(k>2\) and diameter d. Suppose further that G is not a complete multipartite graph. let \(\theta\) be an eigenvalue of G with \(\theta \neq Ik,\) and \(m>1\). Then there are only finitely many connected, co-connected distance regular graphs with an eigenvalue of multiplicity m.
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A Bound for the Diameter of Distance-Regular Graphs

Combinatorica, 1999
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