TY - JOUR T1 - Some Algebraic and Combinatorial Properties of the Complete $T$-Partite Graphs TT - JF - IJMSI JO - IJMSI VL - 13 IS - 1 UR - http://ijmsi.ir/article-1-788-en.html Y1 - 2018 SP - 131 EP - 138 KW - Cohen-Macaulay KW - shellable KW - vertex decomposable KW - edge ideal N2 - In this paper, we characterize the shellable complete $t$-partite graphs. We also show for these types of graphs the concepts vertex decomposable, shellable and sequentially Cohen-Macaulay are equivalent. Furthermore, we give a combinatorial condition for the Cohen-Macaulay complete $t$-partite graphs. M3 ER -