For a connected planar simple graph G=(V, E) with e=|E|=16 and v=|V|=9, then find the number of regions that are created when drawing a planar representation of the graph?

Q. Suppose G be a connected planar graph of order n≥5 and size m. If the length of the smallest cycle in G is 5, then which of the following is true?

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Q. What is the number of edges of the greatest planar subgraph of K₃,₂ where m,n≤3?

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Q. A non-planar graph can have ____________

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Q. A direct product of a group G possess which of the following characteristics?

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Q. In invariant algebra, some generators of group G1 that goes either into itself or zero under ______ with any other element of the algebra.

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Q. Which of the following can be embedded in an algebraically closed group?

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Q. Which of the following is the set of m×m invertible matrices?

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Q. If any group is a manifold what is the dimension of that group?

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Q. A Latin square graph is a representation of a _______

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Q. There exists _______ between group homology and group cohomology of a finite group.

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Q. In basic ring theory, any ring R1 may be embedded in its own ________

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Q. In Modern particle physics there must exist ______________

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Q. For any graph say G, Cayley graph is ______________

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