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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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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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Connectivity concerning the last two subconstituents of a Q-polynomial distance-regular graph
Journal of Combinatorial Theory - Series A, 2021J H Koolen
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The Largest Moore Graph and a Distance-Regular Graph with Intersection Array {55, 54, 2; 1, 1, 54}
Algebra and Logic, 2020D V Paduchikh
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On distance-regular graphs Γ of diameter 3 for which Γ 3 is a triangle-free graph
Discrete Mathematics and Applications, 2023Wenbin Guo
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An inequality involving the second largest and smallest eigenvalue of a distance-regular graph
Linear Algebra and Its Applications, 2011Jack Koolen, Jongyook Park
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An automorphism group of a distance-regular graph with intersection array {24, 21, 3; 1, 3, 18}
Algebra and Logic, 2012D V Paduchikh
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An equitable partition for a distance-regular graph of negative type
Journal of Combinatorial Theory Series B, 2005Stefko Miklavic
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