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arXiv · 1402.1002

On Transiso Graph

Vipul Kakkar·Laxmi Kant Mishra
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Abstract

In this note, we define a new graph $\Gamma_d(G)$ on a finite group $G$, where $d$ is a divisor of $|G|$. The vertices of $\Gamma_d(G)$ are the subgroups of $G$ of order $d$ and two subgroups $H_1$ and $H_2$ of $G$ are said to be adjacent if there exists $S_i \in \mathcal{T}(G,H_i)$ $(i=1,2)$ such that $S_1 \cong S_2$. We shall discuss the completeness of $\Gamma_d(G)$ for various groups like finite abelian groups, dihedral groups and some finite $p$-groups.

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Vipul Kakkar, Laxmi Kant Mishra. 2014-02-05. On Transiso Graph. https://arxiv.org/abs/1402.1002

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