1. Let k≥ 1 and G be a k-connected simple graph. Prove that for every SCV(G) with |S| = k + 1, G contains a path containing S. (Hint 1: Fan Lemma can help. Hint 2: Choose a path with the most vertices in S.)

Q: 5. Let G = (V, E) be a finite, connected graph. Show that if no vertex of G has degree less than 2,…

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Q: 1. Let G be a tree and let L be the set of leaves in G (the vertices of degree 1). (a) Suppose that…

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Q: Q5. Suppose G is a graph of order 8 and suppose there are 2 vertices of order 7, 2 vertices of order…

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Q: 2n 4. Prove or disprove: for every n-vertex graph G, x(G) ≤ 2w(G) + a (G) (6 + 10.

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Q: 3. Prove: The sum of valancies ofvertices of a graph I, is twice the number of edges.

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Q: Let Gbe a simple graph with at least 11l vertices, and let G be its complement. (i) Prove that Gand…

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