%0 Journal Article %A Seyyedi, S. M. %A Rahmati, F. %T Some Algebraic and Combinatorial Properties of the Complete $T$-Partite Graphs %J Iranian Journal of Mathematical Sciences and Informatics %V 13 %N 1 %U http://ijmsi.ir/article-1-788-en.html %R %D 2018 %K Cohen-Macaulay, shellable, vertex decomposable, edge ideal, %X 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. %> http://ijmsi.ir/article-1-788-en.pdf %P 131-138 %& 131 %! %9 Research paper %L A-10-1655-1 %+ Amirkabir University of Technology %G eng %@ 1735-4463 %[ 2018