We present an upper bound on the number of vertices in graphs of given degree and diameter 3 that... more We present an upper bound on the number of vertices in graphs of given degree and diameter 3 that arise as lifts of dipoles with voltage assignments in Abelian groups. Further, we construct a family of Cayley graphs of degree d =3 m − 1 and diameter k ≥ 3 of order kmk. By comparison with other available results in this area we show that, for sufficiently large d and k such that k ≤ d − 2, our family gives the current largest known Cayley graphs of degree d and diameter k.
We present an upper bound on the number of vertices in graphs of given degree and diameter 3 that... more We present an upper bound on the number of vertices in graphs of given degree and diameter 3 that arise as lifts of dipoles with voltage assignments in Abelian groups. Further, we construct a family of Cayley graphs of degree d =3 m − 1 and diameter k ≥ 3 of order kmk. By comparison with other available results in this area we show that, for sufficiently large d and k such that k ≤ d − 2, our family gives the current largest known Cayley graphs of degree d and diameter k.
... A d-valent map M on an orientable surface is a Cayley map if and only if M is a regular cover... more ... A d-valent map M on an orientable surface is a Cayley map if and only if M is a regular covering space of a single-vertex d-valent map M 1 on some orientable surface, or equivalently, M can be obtained as a lift of M 1 by a suitable voltage assignment on the dart set of M 1 in ...
We present an upper bound on the number of vertices in graphs of given degree and diameter 3 that... more We present an upper bound on the number of vertices in graphs of given degree and diameter 3 that arise as lifts of dipoles with voltage assignments in Abelian groups. Further, we construct a family of Cayley graphs of degree d =3 m − 1 and diameter k ≥ 3 of order kmk. By comparison with other available results in this area we show that, for sufficiently large d and k such that k ≤ d − 2, our family gives the current largest known Cayley graphs of degree d and diameter k.
We present an upper bound on the number of vertices in graphs of given degree and diameter 3 that... more We present an upper bound on the number of vertices in graphs of given degree and diameter 3 that arise as lifts of dipoles with voltage assignments in Abelian groups. Further, we construct a family of Cayley graphs of degree d =3 m − 1 and diameter k ≥ 3 of order kmk. By comparison with other available results in this area we show that, for sufficiently large d and k such that k ≤ d − 2, our family gives the current largest known Cayley graphs of degree d and diameter k.
... A d-valent map M on an orientable surface is a Cayley map if and only if M is a regular cover... more ... A d-valent map M on an orientable surface is a Cayley map if and only if M is a regular covering space of a single-vertex d-valent map M 1 on some orientable surface, or equivalently, M can be obtained as a lift of M 1 by a suitable voltage assignment on the dart set of M 1 in ...
Uploads
Papers by Jana Šiagiová