arXiv subjects
Publications and source records attributed to Laxmi Kant Mishra.
Transiso graph $Γ_d(G)$ is defined in for a finite group $G$ and a divisor $d$ of $|G|$. In the present paper, we have determined some finite groups $G$ for which the graphs $Γ_d(G)$ are complete for each divisor $d$ of $|G|$. We have also discussed the completeness of transiso graphs for the groups of order less than $32$.
In this note, we define a new graph $Γ_d(G)$ on a finite group $G$, where $d$ is a divisor of $|G|$. The vertices of $Γ_d(G)$ 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 $Γ_d(G)$ for various groups like finite abelian groups, dihedral groups and some finite $p$-groups.