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[[less than or equal to].sub.x] is a partial order relation.
Recall that a comparability graph is a simple undirected graph G = G(V, E) for which there exists a partial order on V under which two different vertices u, v [member of] V are comparable if and only if {u, v} [member of] E.
As usual, [less than or equal to] denotes the natural partial order on S.
Let (X,p) be a complete dualistic partial metric space, [phi]: X [right arrow] R be a bounded below function and "[less than or equal to]" be the partial order induced by [phi].
Xueming Ren and X.L.Ding, The natural partial order on U-semiabundant semigroups, Scientia Magna, 3(2007), 422-462.
In this section, we will firstly introduce the natural partial order on semiabundant semigroups, and then give some properties for the partial order.
In this paper, we will introduce the natural partial order on U-semiabundant semigroups and describe the properties of such semigroups by using the natural partial order.
He covers a common framework for discrete structures, graphs and directed graphs, preorders and partial orders, hypergraphs, and complexes and multicomplexes.
Shipping has been expedited for the purchaser to ship full or partial orders to one or multiple dealership locations or customers.
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