The order supergraph of the power graph of a finite group

Authors

ASMA HAMZEH
ALI REZA ASHRAFI

DOI

10.3906/mat-1711-78

Abstract

The power graph $\mathcal{P}(G)$ is a graph with group elements as a vertex set and two elements are adjacent if one is a power of the other. The order supergraph $\mathcal{S}(G)$ of the power graph $\mathcal{P}(G)$ is a graph with vertex set $G$ in which two elements $x, y \in G$ are joined if $o(x) o(y)$ or $o(y) o(x)$. The purpose of this paper is to study certain properties of this new graph together with the relationship between $\mathcal{P}(G)$ and $\mathcal{S}(G)$.

Keywords

Power graph, order supergraph, proper order supergraph

First Page

1978

Last Page

1989

Recommended Citation

HAMZEH, ASMA and ASHRAFI, ALI REZA (2018) "The order supergraph of the power graph of a finite group," Turkish Journal of Mathematics: Vol. 42: No. 4, Article 34. https://doi.org/10.3906/mat-1711-78
Available at: https://journals.tubitak.gov.tr/math/vol42/iss4/34