# Description of the Orders Which are Hereditarily Half-reconstructible by Their Comparability Graphs

Abstract: Let P and P' be two orders on the same set X. The order P' is hemimorphic to P if it isomorphic to P or to its dual P*. It is hereditarily hemimorphic to P if for each subset A of X, the orders P↿A and P'↿A induced on A are hemimorphic. The order P is hereditarily half-reconstructible by its comparability graph if it is hereditarily hemimorphic to each order Q on X having the same comparability graph as P. In this paper, we begin by obtaining a new result on the decomposition of orders. Then we use this result to describe the orders which are hereditarily half-reconstructible by their comparability graphs. By the last result we solve an open problem posed in 2013, by Alzohairi, Bouaziz, and Boudabbous.

Excess properties calculated from the experimental values of densities and viscosities have been presented in the previous work.

Abstract: Let P and P' be two orders on the same set X. The order P' is hemimorphic to P if it isomorphic to P or to its dual P*. It is hereditarily hemimorphic to P if for each subset A of X, the…

A finite order P on a set V is reconstructible (respectively, reconstructible up to duality) by its comparability graph if each order on V which has the same comparability graph as P is isomorphic…