Title : ( A graph associated to a fixed automorphism of a finite group )
Authors: Mansoureh Mahtabi , Ahmad Erfanian ,
Full TextAbstract
Let G be a finite group and Aut(G) be the group of automorphisms of G. We associate a graph to a group G and fixed automorphism a of G denoted by G as follows. The vertex set of G is G n Za(G) and two vertices x; g 2 G n Za(G) are adjacent if [g; x] = 1 or [x; g] = 1, where [g; x] = g 1 x 1 gx and Z (G) = fx 2 G j [g; x] = 1 for all g 2 Gg. In this paper, we state some basic properties of the graph, like connectivity, diameter, girth and Hamiltonian. Moreover, planarity and 1-planarity are also investigated here.
Keywords
, Automorphism group, diameter , independent set, dominating set, planer, outer planar.
@article{paperid:1067070,
author = {Mahtabi, Mansoureh and Erfanian, Ahmad},
title = {A graph associated to a fixed automorphism of a finite group},
journal = {Hacettepe Journal of Mathematics and Statistics},
year = {2018},
volume = {4},
number = {46},
month = {January},
issn = {1303-5010},
pages = {93--99},
numpages = {6},
keywords = {Automorphism group; diameter ; independent set; dominating set;
planer; outer planar.},
}
%0 Journal Article
%T A graph associated to a fixed automorphism of a finite group
%A Mahtabi, Mansoureh
%A Erfanian, Ahmad
%J Hacettepe Journal of Mathematics and Statistics
%@ 1303-5010
%D 2018
