%0 Journal Article %T Equigeodesics on full, $G_2$ and a rank-three condition on flag manifolds %A Lino Grama %A Caio J. C. Negreiros %A Neiton P. Silva %J Mathematics %D 2010 %I arXiv %X This paper provides a characterization and examples of homogeneous geodesics on full $G/T$ and $G_{2}$ flag manifolds. We discuss for generalized root systems the property of sum-zero triple of $T$-roots and give several applications of this result. %U http://arxiv.org/abs/1010.4246v2