Q. An undirected graph has 8 vertices labelled 1, 2, …,8 and 31 edges. Vertices 1, 3, 5, 7 have degree 8 and vertices 2, 4, 6, 8 have degree 7. What is the degree of vertex 8?

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Q. G is an undirected graph with n vertices and 26 edges such that each vertex of G has a degree at least 4. Then the maximum possible value of n is ___________

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Q. Hasse diagrams are first made by ______

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Q. If a partial order is drawn as a Hasse diagram in which no two edges cross, its covering graph is called ______

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Q. If the partial order of a set has at most one minimal element, then to test whether it has a non-crossing Hasse diagram its time complexity __________

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Q. Which of the following relation is a partial order as well as an equivalence relation?

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Q. The relation ≤ is a partial order if it is ___________

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Q. In which of the following relations every pair of elements is comparable?

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Q. In a poset (S, ⪯), if there is no element n∈S with m<n, then which of the following is true?

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Q. In a poset P({v, x, y, z}, ⊆) which of the following is the greatest element?

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Q. Suppose P₁ is a partially ordered class and a cut of P₁ is pair (D, T) of nonempty subclasses of P₁ satisfies which of the following properties?

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Q. Let G be the graph defined as the Hasse diagram for the ⊆ relation on the set S{1, 2,…, 18}. How many edges are there in G?

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Q. A Poset in which every pair of elements has both a least upper bound and a greatest lower bound is termed as _______

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Q. In the poset (Z⁺, |) (where Z⁺ is the set of all positive integers and | is the divides relation) are the integers 9 and 351 comparable?

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Q. If every two elements of a poset are comparable then the poset is called ________

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Q. ______ and _______ are the two binary operations defined for lattices.

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Q. A ________ has a greatest element and a least element which satisfy 0<=a<=1 for every a in the lattice(say, L).

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Q. A sublattice(say, S) of a lattice(say, L) is a convex sublattice of L if _________

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Q. Every poset that is a complete semilattice must always be a _______

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Q. A free semilattice has the _______ property.

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