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Memristance and transmemristance in multiterminal memristive systems
Milano G +5 more
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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. +2 more
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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. +2 more
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1978
Inequalities are obtained between the various parameters of a distance-regular graph. In particular, if k1 is the valency and k2 is the number of vertices at distance two from a given vertex, then in general k1 ⩽ k2. For distance-regular graphs of diameter at least four, k1=k2 if and only if the graph is simply a circuit.
D. E. Taylor, Richard Levingston
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Inequalities are obtained between the various parameters of a distance-regular graph. In particular, if k1 is the valency and k2 is the number of vertices at distance two from a given vertex, then in general k1 ⩽ k2. For distance-regular graphs of diameter at least four, k1=k2 if and only if the graph is simply a circuit.
D. E. Taylor, Richard Levingston
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Bipartite distance-regular graphs. II
Graphs and Combinatorics, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Eigenpolytopes of Distance Regular Graphs
Canadian Journal of Mathematics, 1998AbstractLet 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, 1988The 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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Bipartite Q -Polynomial Distance-Regular Graphs
Graphs and Combinatorics, 2004Let \(\Gamma\) denote a bipartite \(Q\)-polynomial distance-regular graph with diameter \(D\geq 4\). Then the intersection numbers of \(\Gamma\) are determined by \(D\) and two real scalars \(q\) and \(s^*\). It is proved that \(s^*=0\) if \(D\geq 12\). Theorem 1.1. Let \(\Gamma\) be a bipartite distance-regular graph with diameter \(D\geq 12\). Then \(
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Codes in Shilla Distance-Regular Graphs
Proceedings of the Steklov Institute of Mathematics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Potential Theory on Distance-Regular Graphs
Combinatorics, Probability and Computing, 1993A graph may be regarded as an electrical network in which each edge has unit resistance. We obtain explicit formulae for the effective resistance of the network when a current enters at one vertex and leaves at another in the distance-regular case.
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