On Co-Maximal Subgroup Graph of $D_n$

Document Type : Original paper

Authors

1 Department of Mathematics, Presidency University, Kolkata 86/1, College Street, Kolkata 700073

2 School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar

Abstract

Let $G$ be a group and $S$ be the collection of all non-trivial proper subgroups of $G$. The co-maximal subgroup graph $\Gamma(G)$ of a group $G$ is defined to be a graph with $S$ as the set of vertices and two distinct vertices $H$ and $K$ are adjacent if and only if $HK=G$. In this paper, we study the comaximal subgroup graph on finite dihedral groups. In particular, we study order, maximum and minimum degree, diameter, girth, domination number, chromatic number and perfectness of comaximal subgroup graph of dihedral groups. Moreover, we prove some isomorphism results on comaximal subgroup graph of dihedral groups.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 31 January 2024

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