The Action of $$SL(2,{\mathbb {C}})$$ S L ( 2 , C ) on Hyperbolic 3-Space and Orbital Graphs

Beşenk, Murat

doi:10.1007/s00373-018-1893-9

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2020

2024

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“…He also determined the infinite families of orbital graphs with a diameter of 2. The action of SL(2, C) on hyperbolic 3-space and orbital graphs was first observed by Besenk [7]. Recently, Nagnibeda et al [8] published an article where they show interest in orbital graphs for the action of spinal groups on d-regular rooted trees and on their boundaries.…”

Section: Introductionmentioning

confidence: 99%

On the Orbital Regular Graph of Finite Solvable Groups

Sharma,

Bhat,

Singh

2024

Util. Math.

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Let G be a finite solvable group and Δ be the subset of Υ×Υ, where Υ is the set of all pairs of size two commuting elements in G. If G operates on a transitive G – space by the action (υ1,υ2)g=(υg1,υg2); υ1,υ2∈Υ and g∈G, then orbits of G are called orbitals. The subset Δo={(υ,υ);υ∈Υ,(υ,υ)∈Υ×Υ} represents G′s diagonal orbital.The orbital regular graph is a graph on which G acts regularly on the vertices and the edge set. In this paper, we obtain the orbital regular graphs for some finite solvable groups using a regular action. Furthermore, the number of edges for each of a group’s orbitals is obtained.

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Section: Introductionmentioning

confidence: 99%