Equigeodesic vectors on compact homogeneous spaces with equivalent isotropy summands

In this paper, we investigate equigeodesics on a compact homogeneous space $M=G\mathrm{/}H\mathrm{.}$ We introduce a formula for the identification of equigeodesic vectors only relying on the isotropy representation of $M$ and the Lie structure of the Lie algebra of $G$. Applications to $M$-spaces are also discussed.