Journal of Prime Research in Mathematics, Volume (11), No (1), Year (2015-12) , Pages (55-60)

#### Title : ( The Complement of Subgroup Graph of a Group )

Authors: fereshteh kakeri , Ahmad Erfanian ,

Citation: BibTeX | EndNote

Let $G$ be a finite group and $H$ a subgroup of $G$. In 2012, David F. Anderson et al. introduced the subgroup graph of $H$ in $G$ as a simple graph with vertex set consisting all elements of $G$ and two distinct vertices $x$ and $y$ are adjacent if and only if $xy \in H$. They denoted this graph by $\Gamma_H(G)$. In this paper, we consider the complement of ${\Gamma}_H(G)$, denoted by $\overline{\Gamma_H(G)}$ and will give some graph properties of this graph, for instance diameter, girth, independent and dominating sets, regularity. Moreover, the structure of this graph, planerity and 1-planerity are also investigated in the paper.

#### Keywords

, Subgroup graph, complement of subgroup
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@article{paperid:1055230,
author = {Kakeri, Fereshteh and Erfanian, Ahmad},
title = {The Complement of Subgroup Graph of a Group},
journal = {Journal of Prime Research in Mathematics},
year = {2015},
volume = {11},
number = {1},
month = {December},
issn = {1817-3462},
pages = {55--60},
numpages = {5},
keywords = {Subgroup graph; complement of subgroup graph},
}