Let n € N with n > 2 and let G₁ = (V, E) be the graph with vertex set V = {₁, V2, ..., V2n} and edge set E = {{v₂, vi+1} : 1 ≤ i ≤ 2n-1}U {v₁, V2n}¯ {{Vi, Vn+i} | 1

Q: 8. (a) Can you draw a graph with at least two vertices for which all the vertices have different…

A: consider the graph  A has valence 1 Vertex B has valence 2 Vertex C has Valence 3 Vertex D has…

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

A:

Q: 2. Graph y = 1+ 2sin (x- n) on 0 < x < 6TI.

A:

Q: Let G be a graph with n 1 vertices. (a) If x(G) = 1, what can you say about E(G), the edge set of G?…

A: Given : G is a graph with n≥1 vertices We have to answer the following : (a) If χG=1, what can be…

Q: Show that For n > 1 let G, be the simple graph with vertex set V(Gn) = {1,2,., n} in which two…

A: A simple connected graph G is said to be planar if we can draw the graph in the plane with no two…

Q: A simple graph is called regular if every vertex of the graph has the same degree. An n-regular…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 3.(a) Draw C6, C7, We and W7. 3.(b) Are C, and W, regular graphs? Justify your answer. 3.(c) How…

A:

Q: 14. Let G be the graph with vertices v1, v2, and v3 as shown below. What is the number of walks of…

A: Walk :- A walk in graph is a sequence of vertices and edges.

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

A: There is n -vertex graph G. For the n vertex graph G, it has to be proven that χ(G) ≤2ω(G) + 2n/α(G)…

Q: D) show graph y=1/(3-x) and y=P3(x

A: A Maclaurin series is given by                               f(x)=∑k=0∞fk(a)k!xk…

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: 3) Let f(x,y) = 9x² + y² Statch the graph of fl

A: Sketch the graph of f(x,y)=9x2+y2

Q: • A simple graph is called regular if every vertex of the graph has the same degree. An N-regular…

A:

Q: Let G = (V, E) be a graph and A = max,ev{deg(v)}. Show that x(G) <A+1. Give two examples of graphs…

A:

Q: Let G be a simple graph that satisfies the following three conditions: (1) the graph G has 12…

A: Since the minimum degree (G) is at least 1, we know that each vertex in the graph has to be…

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

A:

Q: can you please provide explanations

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

Q: Let P₁ and P₂ be two paths of maximum length in a connected graph G. Prove that P₁ and P2 have a…

A: First, we need to understand the problem. We are given two paths P1 and P2 of maximum length in a…