Geodesic
A note on constructing large Cayley graphs of given degree and diameter by voltage assignments
The electronic journal of combinatorics, Tome 5 (1998)
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Voltage graphs are a powerful tool for constructing large graphs (called lifts) with prescribed properties as covering spaces of small base graphs. This makes them suitable for application to the degree/diameter problem, which is to determine the largest order of a graph with given degree and diameter. Many currently known largest graphs of degree $\le 15$ and diameter $\le 10$ have been found by computer search among Cayley graphs of semidirect products of cyclic groups. We show that all of them can in fact be described as lifts of smaller Cayley graphs of cyclic groups, with voltages in (other) cyclic groups. This opens up a new possible direction in the search for large vertex-transitive graphs of given degree and diameter.
DOI : 10.37236/1347
Classification : 05C25
Mots-clés : base graphs, diameter problem, Cayley graphs, cyclic groups, voltages, vertex-transitive graphs 
@article{10_37236_1347,
     author = {Ljiljana Brankovi\'c and Mirka Miller and J\'an Plesn{\'\i}k and Joe Ryan and Jozef \v{S}ir\'a\v{n}},
     title = {A note on constructing large {Cayley} graphs of given degree and diameter by voltage assignments},
     journal = {The electronic journal of combinatorics},
     year = {1998},
     volume = {5},
     doi = {10.37236/1347},
     zbl = {0885.05071},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1347/}
}
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Ljiljana Branković; Mirka Miller; Ján Plesník; Joe Ryan; Jozef Širáň. A note on constructing large Cayley graphs of given degree and diameter by voltage assignments. The electronic journal of combinatorics, Tome 5 (1998). doi: 10.37236/1347

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