Geodesic
A conjecture of Biggs concerning the resistance of a distance-regular graph
The electronic journal of combinatorics, Tome 17 (2010)
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Biggs conjectured that the resistance between any two points on a distance-regular graph of valency greater than 2 is bounded by twice the resistance between adjacent points. We prove this conjecture, give the sharp constant for the inequality, and display the graphs for which the conjecture most nearly fails. Some necessary background material is included, as well as some consequences.
DOI : 10.37236/350
Classification : 05E30, 05C12 
@article{10_37236_350,
     author = {Greg Markowsky and Jacobus Koolen},
     title = {A conjecture of {Biggs} concerning the resistance of a distance-regular graph},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/350},
     zbl = {1225.05256},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/350/}
}
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Greg Markowsky; Jacobus Koolen. A conjecture of Biggs concerning the resistance of a distance-regular graph. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/350

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