Study of Algebraic Properties of Pseudo-Complete Graphs

In this paper we introduce a class of graphs, named pseudo-complete graphs, which are not complete, but near to complete graphs obtained by gluing of two complete graphs over a complete graph. Then we study some combinatorial and algebraic properties of these graphs. We will provide explicit formula to compute some properties of these graphs such as height, Krull dimension, projective dimension, regularity, depth in terms of those of the original graphs.