Graph with given automorphic group and given nuclear number
DOI:
https://doi.org/10.22199/S07160917.1992.0001.00004Keywords:
automorphism, graphsAbstract
In 1938, Frucht proved that every finite group may be represented by a graph; in other words, given any finite group H, there is graph G whose automorphism group is isomorphic to H. Starting from this result a great many mathematicians have studied the following problem: "Given a finite group H and given a property P, is there a graph G that represents H and that satisfies the property P ?"
The aim of this paper is to solve a problem of such characteristics. The statement we get is the following: "Every finite group H may be represented by a graph G whose nuclear number is n ? 2 , where n is a given positive integer "
References
[ 2] Frucht, R.: Herstellung von Graphen mit vorgegebener abstrakter Gruppe, Compositio Math., 6, 239-250, 1938.
[ 3] Montenegro, E.: Un resultado sobre el orden y el tamaño de grafos que representan a un grupo finito, Visiones Científicas, 2, 49-71, 1986, Valparaíso, Chile.
[ 4] Sabidussi, G.: Graphs with given group and given graph-theoretical properties, Canad. J. Math., 9, 515-525, 1957.
Published
How to Cite
Issue
Section
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
