What is a(G) if G is a complete graph on n vertices?

Q: If a simple graph G is having 15 vertices and 5 edges then its complement graph G will have None of…

A: 15 vertices and 105 edges

Q: Find all r-regular graphs of order n for a convenient selection of r, n.

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Q: G – v3 G- v2 G – v4

A: A graph consist of Set of vertices and edges A subgraph W of a graph G consist of subset of edges…

Q: not use ai please

A: Step 1: It is given that n is even. Let the two components have m and n−m vertices, respectively.…

Q: Let G be a simple connected 6-regualar graph with 50 vertices. Then G is (i) a planar graph (ii) a…

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Q: Consider a complete graph with 6 vertices labeled A, B, F. (a) If you can start at any vertex, how…

A: Step-1 Consider a graph with 6 vertices, For complete graph with n vertices there exist   n-1!2…

Q: (d) Show that the pair of graphs are not isomorphic by showing that there is a property that is…

A: (d)  To prove that the pair of graphs are not isomorphic by showing that there is        a property…

Q: Let G be a simple undirected graph. Prove that (a) if G is disconnected, then d(GC) ≤ 2; (b) if d(G)…

A: Given: G is a simple undirected graph.To prove: a) d(Gc)≤2 if G is disconnected.                 b)…

Q: in fuzzy graph theory What is the transitive And give examples

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Q: B\ Let G be a simple graph. Show that if G is not connected, then it's complement G is connected.

A: Let G be a simple graph.  Let G be not connected.  Now, we know that a graph is connected iff…

Q: Let G be a graph such that every vertex has degree 4 and the number of edges is 12. How many…

A: In the given problem we apply Euler's formula for polygon V - E + F = 2 Where V is the vertices of…

Q: Let Vn be the set of connected graphs having n edges, vertex set [n], and exactly one cycle. Form a…

A: Given Let Vn be the set of connected graphs having n edges, vertex set [n], and exactly one cycle.…

Q: Don't use chat gpt It Chatgpt means downvote

A: Step 1: Step 2: Step 3: Step 4:

Q: Approximate the volume of the solid in the first octant bounded by the sphere x² + y² + z² = 64, the…

A: We have to find an approximate the volume of the solid in the first octant bounded by the sphere…

Q: State and prove closed graph theorem

A: The closed graph theorem is given as follows :

Q: . Let G be a graph with V = {1,2, 3, 4, 5, 6} and no edge between an odd and even vertex (a) Draw…

A: Given that V={1,2,3,4,5,6} a) draw the graph G with the maximum number of edges b) How many…

Q: Use Mathemafica to sketch graph of gaez and 1)

A: The required graphs are shown below

Q: At a cupcake stall at the Greenwich market, the owner is selling six different types of cupcakes.…

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Q: (4) Show that it is not possible to define a graph with 5 vertices of degree 3, and 2 vertices of…

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Q: Show that, in a graph G, i(G)-set is different to t(G)-set.

A: As per the question we have to show that for any planner graph G we will have the i(G) set is…

Q: Let G be a simple graph with n vertices and k connected components. Find the maximum and the minimum…

A: The objective of this question is to find the maximum and minimum possible number of edges in a…

Q: How can I prove "A graph is k-colourable if and only if it is k-partite.”?

A: As per the question we have to prove that a graph is k-colourable if and only if it is k-partite. To…

Q: Prove that for any graph on n vertices, a k-regular graph can never be a tree. (Graph Theory)

A: Proof: In a k-regular graph, the degree of each vertex must be k, which means each vertex must be…

Q: (b) Show that G may not necessarily have three cycle subgraphs by giving an example of a graph G,…

A: Consider the equation

Q: Suppose G is a simple connected graph such that G is unicyclic. Prove that |V (G)| = |E(G)|.…

A: A cyclic graph has minimum of 3 vertices which is connected in a cycle and a graph is unicyclic…

Q: Write a function that returns true (1) if u and v have an edge in a directed graph represented by…

A: Since you are not mentioning the programming language, here we are using C++ to complete the…

Q: 4a Let n > 4. What is the maximum possible number of edges in a graph with n vertices and n-2…

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Q: Let G be a graph with 10 vertice and 5 components. If a vertex is removed from G, the number of…

A: Answer: 9 and 4

Q: can you please provide explanations

A: 1. Assumption: Start with the assumption that (G1​) and (G2​)are isomorphic graphs. 2. Definition of…

Q: Prove or disprove: There exists some n > 1 such that there is a simple graph on n vertices, where…

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Q: If G is a graph, then the sum of its vertex degrees is nonnegative and even.

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Q: A graph G is simple if O (c) It is not contain loop or multiple edges. O (d) It is not contains a…

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Q: Give a family of graphs of order p such that t(G) = 2.

A: The family of graphs of order p such that γtG=2 are given below.

Q: True or false: If a connected graph G can be decomposed into exactly k paths then exactly 2k…

A: To Prove: A connected graph can be decomposed into exactly k paths then exactly 2k vertices of G…

Q: 2°) Use integration by parts to prove that, for any positive integer n, (2n + 1) In = 2n In-1. 3°)…

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Q: prove If G is a plane graph with n vertices, m edges and r regions, then n - m + r = 1 + k(G).

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Q: [1] Write down the vertex-connectivity K(G) and the edge-connectivity 2(G) for each of the following…

A: Vertex connectivity: The minimum number of vertices required to disconnect the graph G is called…