On Transiso Graphs of Groups of order less than 32

TL;DR

This paper investigates the properties of transiso graphs for finite groups of order less than 32, identifying conditions under which these graphs are complete, and providing a classification for small groups.

Contribution

It determines which finite groups of order less than 32 have complete transiso graphs for all divisors of their order, expanding understanding of these graph structures.

Findings

Identified groups with complete transiso graphs for each divisor of their order.

Classified groups of order less than 32 based on transiso graph completeness.

Extended previous results to small finite groups.

Abstract

Transiso graph $\Gamma_d(G)$ 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 $\Gamma_d(G)$ are complete for each divisor $d$ of $|G|$. We have also discussed the completeness of transiso graphs for the groups of order less than $32$.