Q7. For Theorems below give an example tree T with 15 vertices. Theorem 1. If a tree T is a wounded spider of order p, then y(T) = p - A(T). Theorem 2. If G is a connected graph, then [ diam (G)+¹1 ≤ (G). 3

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A: Given  y1, y2, ...... yd are children inthe order they were added to the tree.  We have to show that…

Q: 3. Let T, = (v,e,) and T, = (v,e,) be two trees with e, = 12 and v, = 3 + 5v,. Find: and Remember: e…

A: As e=v-1 e1=v1-1⇒12=v1-1⇒v1=12+1=13v2=3+5v1=3+513=3+65=68e2=v2-1=68-1=67

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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: Find all maximal independent sets of path Pio and C10.

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Q: . Sketch the graph of the set defined by A x B where A is the closed interval [-2, 4] and B = {1, 3,…

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Q: Please do the following questions with handwritten working out

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Q: Lemma 1 Consider a node x with rank (number of children) d. Let y1, Y2, ..., Yd be those children in…

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Q: Let G = (V, E) be a finite bipartite graph with bipartition (A, B) where DI

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Q: Suppose G is a simple connected graph with 12 vertices and 16 edges. Suppose 4 of its vertices are…

A: note :Since you have posted multiple questions, we will provide the solution only to the first…

Q: Let G be a simple graph (no loops or multi-edges) and G' denote the complement of G. It is known…

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Q: Suppose we add two edges in a tree T to form a graph G. How many cycles can be there in G.

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A: Answer (1) E = { (u,v) , u, v ∈ V | person u and V have met each other}(2) degree of a vertex u of G…

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Q: Discrete MAth Graph Theory and spanning tree Let G be a connected graph, and let T1, T2 be two…

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Q: 2. Draw all non-isomorphic trees of order n, where 2 < n < 6.

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Q: Select all that are true. a) For any bipartite graph G = (LUR, E), if |L| = |R| then ElEL deg(l) =…

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Q: 7. Prove: "If T is a tree of order n and size m, then m = n – 1." Give a concrete example to…

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Q: 8) Consider the directed graph below 1 point Ps P1 P2 PA The number of 2-step connections for this…

A: The adjacency matrix is given by A = 0010100010010100000101000 Then  A2 = 0010100010010100000101000…

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